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There are some questions on mathoverflow such as

with answers that tell us things such as:

Mathematicians prefer to use older books because of some old books are full of amazing ideas and some of them are comprehensive (such as books of Spivak).

Question: What older books (with low quality typesetting) would you like to see reprinted with high quality typesetting?

My question is not just a question. We are a group of math students (most of them are geometry students) that want to re-write popular old books using $\mathrm{\LaTeX}$.

One can search for most cited books such as: Curvature and Betti numbers (K Yano, S Bochner) or Einstein manifolds (AL Besse).

Update: We have some rules:

  1. After sending $\LaTeX$ and PDF file of rewritten books to main author or publisher, we delete it from our computer.

  2. We never publish it anywhere on internet (If publisher or author give an answer for re-typing).

  3. We don't want to earn money by selling these books (If publisher or author didn't accept to pay for our work we have no way but creating a donation page after author or publisher approval).

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    $\begingroup$ wouldn't you run into copyright restrictions? (it typically takes author's life time + 70 years to expire...) $\endgroup$
    – Carlo Beenakker
    Commented Dec 17, 2018 at 8:21
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    $\begingroup$ I'm afraid not without asking permission from copyright holders. $\endgroup$
    – Carlo Beenakker
    Commented Dec 17, 2018 at 9:44
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    $\begingroup$ I'm surely not the only one who hopes you'll do it anyway. $\endgroup$
    – Harry Gindi
    Commented Dec 17, 2018 at 11:21
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    $\begingroup$ Project Gutenberg (edit: a non-profit that exists to enable electronic access to public domain works) has a helpful FAQ about re-releasing works (in the US) without copyright restrictions. The "easy" standard is any edition published before 1923 is always fine, with some exceptions for more recent works. See gutenberg.org/wiki/Gutenberg:Copyright_FAQ and of course, consult a lawyer. $\endgroup$
    – Ben Burns
    Commented Dec 17, 2018 at 14:56
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    $\begingroup$ Besse's Einstein Manifolds has excellent quality typesetting, so perhaps you would rather mention something older, like Bott's beautiful Lectures on Characteristic Classes and Foliations. $\endgroup$
    – Ben McKay
    Commented Dec 17, 2018 at 15:14

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Morse Theory by Milnor (and Spivak and Wells)

$\color{blue}{\text{Typesetting of this book has been finished}}$. Read it online here

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    $\begingroup$ Yes, and with modern notation. $\endgroup$
    – Michael
    Commented Dec 17, 2018 at 17:06
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    $\begingroup$ Isn’t the notation pretty modern? Or am I just too old? $\endgroup$
    – Deane Yang
    Commented Dec 18, 2018 at 6:12
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    $\begingroup$ @C.F.G I think it would be most natural that you approach him yourself — it's your project/idea after all. You can ask him whether he would welcome such an idea and if he does, either he could talk to the publisher directly, or you could tell the publisher that the author of the books would support your project. $\endgroup$
    – Earthliŋ
    Commented Dec 26, 2018 at 10:58
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    $\begingroup$ I think that the natural person to approach about undertaking such a project would be Michael Spivak. He still runs Publish or Perish, the last I knew, and he's a LaTeX guru who actually did typeset his Comprehensive Introduction to Differential Geometry. At the very least, I think that he'd give you some valuable advice. $\endgroup$
    – Robert Bryant
    Commented Jan 2, 2019 at 12:36
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    $\begingroup$ Because Publisher and Author of this book Leaved my email without any response I'll Publish it freely. Download It from here: oldbookstonew.blogspot.com. $\endgroup$
    – C.F.G
    Commented Mar 16, 2019 at 19:58
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I have some experience resurrecting old math books and I want to make a few comments about copyright.

First, it is definitely true that except for very old books, someone owns the copyright. Typically it's the publisher, although sometimes it's the author. (If it's a collection of articles by multiple authors then the copyright may be shared in some complicated way.) In some cases, it's not actually clear who owns the copyright, e.g., because the publisher was bought out by another publisher and some of the paperwork was misplaced. But in any case, usually you should start by presuming that the publisher owns the copyright.

What are the implications of copyright? First, there's really nothing stopping you from creating a $\mathrm{\LaTeX}$ version of a book for your own personal use. It's only when you want to post it on the web or share it with someone else that copyright issues rear their head. So one approach you can take is to do all the work, and then approach the copyright holder and hope that they will agree to publish your new version. Note that if you do this, then the copyright holder is under no obligation to pay you for your work or give you royalties or anything like that.

Another possibility is to approach the copyright holder before doing any work and reach some sort of agreement ahead of time. The advantage of doing this is that you know what you are getting yourself into before you put in a lot of work. Be aware that even if the book gets republished and it sells well, you're unlikely to see much if any of that money.

Either way, be aware that the copyright holder is under no obligation to do you any favors. If they elect not to republish the book then legally there's not much you can do about that. If you've already created the $\mathrm{\LaTeX}$, they could demand that you hand it over (EDIT in response to comments: Such a demand will typically not be legally enforceable but they may issue it anyway as an intimidation tactic), and if you comply, they may then sit on it without publishing it or releasing the copyright to anyone else.

Having said all this, I don't mean to say that you shouldn't go ahead with your plans. I have successfully managed to get a couple of old math books republished. It was more work than I initially expected (even though I didn't have to do any typesetting) and I didn't ask for or receive a dime, but I did get the satisfaction of seeing the books resurrected.

Finally, as others have already mentioned, if you're going to all this trouble then you might want to consider not just re-typesetting but also correcting as many errors as possible.

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    $\begingroup$ The claims that they can "demand you hand it over" and that they have "no obligation to pay you" seems dubious. If you produce a derived work, the copyright holder for the original work does not automatically obtain rights to it, but of course you have no rights to reproduce or distribute it either. There is certainly room for negotiating compensation, although socially/career-wise it may be a very bad idea to try to do so. $\endgroup$
    – R.. GitHub STOP HELPING ICE
    Commented Dec 18, 2018 at 5:19
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    $\begingroup$ Work on it in secret, release it anonymously, and the internet will make sure it never disappears. $\endgroup$
    – Harry Gindi
    Commented Dec 18, 2018 at 6:45
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    $\begingroup$ @R.. : I think you misunderstand my point. In the U.S. at least, free speech is protected by the First Amendment. Therefore the publisher is not doing anything criminal by issuing a demand. That does not mean that the publisher can force you to comply with the demand. I'm just trying to tell you what kinds of behavior you might encounter. I've learned the hard way that publishers do not always behave reasonably. A lot of people are surprised at the behavior they encounter from companies when it comes to copyright and I'm just forewarning people. $\endgroup$
    – Timothy Chow
    Commented Dec 18, 2018 at 21:03
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    $\begingroup$ @TimothyChow: OK, I misunderstood your sense of "can demand", as I think a lot of people would, as a claim that they have legal standing for a court to order you to do so based on their request, rather than just that they have the right to state the "demand". However I think the latter is also shaky. Free speech does not entitle you to make frivilous legal threats to mislead someone into waiving their rights. $\endgroup$
    – R.. GitHub STOP HELPING ICE
    Commented Dec 19, 2018 at 1:08
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    $\begingroup$ I would edit this answer to make sure “demand that you hand it over” is not interpreted as legally enforceable. $\endgroup$
    – user76284
    Commented Dec 19, 2018 at 3:51
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Characteristic Classes by Stasheff and Milnor. Morse Theory by Milnor was already mentioned. Lectures on the h-cobordism theorem would be a nice one. It is also rather short.

These books are published by the Princeton University Press.

  • $\color{blue}{\text{Typesetting of ``Lectures on the h-cobordism theorem (V3 - 2023)" has been finished}}$. Read it online here

  • $\color{blue}{\text{Typesetting of ``Characteristic Classes" has been finished}}$. Read it online here

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Many of the pamphlets produced by Mir publishers (USSR) called (if I recall correctly) the "Little Mathematics Library" were gems to be discovered by High School students. There is an attempt to collect these titles and others from the same publisher.

If these could be reproduced, that would be wonderful for students at that level and the rest of us as well.

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Just for fun, Principia mathematica.

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    $\begingroup$ In modern notation, too? $\endgroup$
    – David Roberts ♦
    Commented Dec 17, 2018 at 20:49
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    $\begingroup$ Sure, so we could tell what it’s about. $\endgroup$
    – Andrej Bauer
    Commented Dec 17, 2018 at 21:02
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    $\begingroup$ Not sure that would be a good idea @DavidRoberts. See, e.g., here (emphasis mine), "This article provides an introduction to the symbolism of PM, showing how that symbolism can be translated into a more contemporary notation which should be familiar to anyone who has had a first course in symbolic logic. This translation is offered as an aid to learning the original notation, which itself is a subject of scholarly dispute, and embodies substantive logical doctrines so that it cannot simply be replaced by contemporary symbolism." $\endgroup$
    – user57432
    Commented Dec 18, 2018 at 4:14
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    $\begingroup$ Someone has already done this one: kickstarter.com/projects/1174653512/… $\endgroup$
    – Joshua Frank
    Commented Dec 19, 2018 at 17:04
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    $\begingroup$ @JoshuaFrank: We are talking about Whitehead and Russell's Principia Mathematica. $\endgroup$
    – user57432
    Commented Dec 20, 2018 at 3:27
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Mumford's Abelian Varieties. (It would also benefit from an expanded index.) However, as noted, you'd need to get permission from whoever holds the copyright.

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    $\begingroup$ There is a LaTeX-typeset edition of this book "published for the Tata Institute of Fundamental Research by the Hindustan Book Agency" and distributed internationally by the AMS. It is available on the AMS website at a list price of $75: bookstore.ams.org/tifr-13 $\endgroup$
    – Bort
    Commented Dec 17, 2018 at 16:03
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    $\begingroup$ @Bort Thanks, I hadn't realized that Tata had reprinted it. I have two copies of the original edition, but they're falling apart! In terms of price, if you're an AMS members, it's only $60 with free shipping. OTOH, for some reason on Amazon there's no link to the AMS site, and lots of 3rd party sellers who are charging hundreds of dollars. $\endgroup$
    – Joe Silverman
    Commented Dec 17, 2018 at 21:48
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    $\begingroup$ The new edition of Abelian Varieties has quite a few typos; thankfully, Brian Conrad has compiled many of them into this list. An older version is available on the Tata Institute website. $\endgroup$
    – Takumi Murayama
    Commented Dec 19, 2018 at 12:37
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    $\begingroup$ @TakumiMurayama : The latest printing now incorporates Brian Conrad's corrections. $\endgroup$
    – Timothy Chow
    Commented May 29, 2020 at 15:54
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    $\begingroup$ @MatthieuRomagny It's on the AMS website, but if you just search for "abelian varieties" in the bookstore, there are so many books with that title, it's not near the top. Searching on "Mumford" brings it up mid-page. In any case, here's the link: bookstore.ams.org/tifr-13 $\endgroup$
    – Joe Silverman
    Commented Apr 28, 2021 at 10:33
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Complexe Cotangent et Déformations I & II by Illusie

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The 1978 book "Probabilities and Potential" by Claude Dellacherie, and Paul-André Meyer (and later volumes) is still a standard reference for man facts concerning probability theory, stochastic processes, and measure theory. Sadly, the typesetting is really ugly and newer reprints are just image copies.

Interestingly, the earlier 1966 book "Probability and Potentials" by Meyer alone, essentially the predecessor, was beautifully typeset.

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  • $\begingroup$ That timing would appear to match what Knuth found with TAoCP, leading to TeX $\endgroup$
    – Chris H
    Commented Dec 19, 2018 at 15:40
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A general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck

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  • $\begingroup$ Is this book used still? its citation is 167 due to Google that seems very low. $\endgroup$
    – C.F.G
    Commented Jul 9, 2019 at 6:11
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    $\begingroup$ @C.F.G it is not used much that is why I would like to get This reprinted. So, people can see.. $\endgroup$
    – Praphulla Koushik
    Commented Jul 9, 2019 at 13:03
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Algebra for Beginners, by Todhunter.

It was first printed 1876, so it should be totally fine to make a typeset version of this. I got an original as a gift, and read it. For a research mathematician, it is elementary, but there is at least one trick that I learned from that book, that high-school (and undergraduate university) did not teach me:

How to simplify $\sqrt{7+4\sqrt{3}}$?

Also, the book is still being printed, latest I can find is from 2016, with a price of about $40 (when ordering from a Swedish company).

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    $\begingroup$ Does the trick have anything to do with period two points of a quadratic function? $\endgroup$
    – JP McCarthy
    Commented Dec 17, 2018 at 12:07
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    $\begingroup$ @JPMcCarthy: The trick is very simple: assume the expression is of the form $\sqrt{x}+\sqrt{y}$ and square both sides, and then see what happens. $\endgroup$
    – Per Alexandersson
    Commented Dec 17, 2018 at 18:56
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    $\begingroup$ @PerAlexandersson which leads to the lovely formula $$\sqrt{a+\sqrt b} = \sqrt{\frac{a-\sqrt{a^2-b}}{{2}}}+\sqrt{\frac{a+\sqrt{a^2-b}}{{2}}}$$ $\endgroup$
    – Greg Martin
    Commented Dec 19, 2018 at 18:34
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    $\begingroup$ By the way, you can find Todhunter's textbook on spherical trigonometry typeset in TeX. gutenberg.org/ebooks/19770 $\endgroup$
    – John D. Cook
    Commented Dec 22, 2018 at 16:11
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    $\begingroup$ @PerAlexandersson Euler explains this trick in his Algebra. Also, it's still taught to secondary school students who take Further Mathematics (in at least my country) under the title of surds. $\endgroup$
    – Allawonder
    Commented Apr 30, 2019 at 17:38
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Borevich-Shafarevich in English or French. Without typos and with modern notation. Please.

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  • $\begingroup$ It seems that this book has good quality typesetting. See here: amazon.com/Number-Theory-Pure-Applied-Mathematics/dp/0121178501 $\endgroup$
    – C.F.G
    Commented Jan 8, 2019 at 5:55
  • $\begingroup$ I have an original copy. Its not a disaster, but it uses some old (and sometimes) ugly notation, and it has many many typos. The book is a masterpiece and it should a pleasure to read in all senses :) $\endgroup$
    – efs
    Commented Jan 8, 2019 at 15:10
  • $\begingroup$ There is a scanned copy. Google "borevich shafarevich", the first link. $\endgroup$
    – efs
    Commented Jan 8, 2019 at 15:11
  • $\begingroup$ The American Mathematical Society looked into "resurrecting" Borevich and Shafarevich and encountered serious copyright obstacles. Not to say that these can't be overcome, but just be aware that you may encounter the same obstacles if you try to resurrect the book yourself. $\endgroup$
    – Timothy Chow
    Commented May 29, 2020 at 15:56
  • $\begingroup$ @TimothyChow Thanks for the update. This "almost resurrection" was a recent event? $\endgroup$
    – efs
    Commented May 29, 2020 at 16:01
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Paul Cohen's Set Theory and the Continuum Hypothesis may be in print, but from the preview on amazon (dot) com it seems to be photographic copy of the one set by a typewritter, with hand-written diacritics.

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All volumes of Asterisque, from 1973 to about 1990.

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    $\begingroup$ Aren’t they finally available online? $\endgroup$
    – LSpice
    Commented Dec 19, 2018 at 13:57
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    $\begingroup$ @LSpice: Yes, but in their original typesetting, mostly by typewriter. $\endgroup$
    – Ben McKay
    Commented Dec 19, 2018 at 14:12
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    $\begingroup$ I feel like if people wanted to do this, they could possibly get an SMF grant. $\endgroup$
    – Harry Gindi
    Commented Dec 19, 2018 at 17:26
  • $\begingroup$ @HarryGindi: Probably or definitely? any link that confirms your comment? $\endgroup$
    – C.F.G
    Commented Oct 28, 2020 at 6:00
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EDIT: The work has been done (thanks @jozefg for noticing). The tex version is available at the blog of one of the authors

The 1977 book of Makkai and Reyes "First-order categorical logic" is an amazing book and still the standard reference for the subject. But the typesetting, and especially the diagrams, are not good. It is readable, but it would be much better if we had a modern edition just for reference. This job has been done for example with some SGA volumes, as part of an ongoing project that aims to retype them in Latex. These are available online through the nlab page.

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Arithmétique des algèbres de quaternions by Marie-France Vigneras

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    $\begingroup$ Yes, although John Voight is writing an encyclopedic masterpiece on Quaternion Algebras. $\endgroup$
    – efs
    Commented Dec 17, 2018 at 14:53
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    $\begingroup$ @EFinat-S It is already written, as Ben likely knows. $\endgroup$
    – Kimball
    Commented Dec 18, 2018 at 0:36
  • $\begingroup$ @Kimball Yes, I meant that in the sense that he is updating it constantly. $\endgroup$
    – efs
    Commented Dec 18, 2018 at 0:45
  • $\begingroup$ maths.nju.edu.cn/~guoxj/notes/qa.pdf $\endgroup$
    – Peter Humphries
    Commented Oct 12, 2020 at 2:39
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Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya

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Masterpieces that deserve at least neat diagrams. After all these years, there is still a lot that one can learn from them and will probably not see it in quite the same extra convenient form anywhere else.

Don't know if any of these are republished - please tell me if they are.

Stable Homotopy and Generalized Homology by J. F. Adams

Just two instances from lots and lots of the brilliant early Springer LNM stuff:

Catégories Cofibrées Additives et Complexe Cotangent Relatif by Grothendieck

The Relation of Cobordism to K-theories by Conner and Floyd

P.S. Many thanks to C.F.G. for delighting update!

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Noel J. Hicks's charming little Notes on Differential Geometry, published by van Nostrand Reinhold in 1965 and reissued in 1971.

Edit (August 11th 2022): As reported by C.F.G in the comments and a previous edit of his, the $\mathsf{\TeX} \mathsf{\text{romancers}}$ group on Discord (cool name, by the way) $\mathsf{\LaTeX}$-ed Hicks's original 1965 issue and released it this year, it is now freely available in PDF format.

I would also add Michael Beals's Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems, published by Birkhäuser in 1989. Its typesetting is absolutely painful to read - it looks like it came out of an old dot-matrix printer.

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    $\begingroup$ I was lucky enough to inherit this from my father. $\endgroup$
    – Deane Yang
    Commented Dec 18, 2018 at 6:11
  • $\begingroup$ I've got an used copy of the 1971 issue, it's incredibly useful. $\endgroup$
    – Pedro Lauridsen Ribeiro
    Commented Dec 18, 2018 at 12:29
  • $\begingroup$ I believe Hicks's little gem serves a different purpose. It's written in a lecture-note style that gets very quickly to the essential results of the subject (much quicker than the admittedly great books you cited - less than 200 short pages!), with minimal prerequisites and only introducing topological hypotheses at the right moment with proper motivation. It also proves some structural results which are difficult to find proven elsewhere - e.g. J.H.C. Whitehead's theorem on the existence of convex normal neighborhoods for (non necessarily Riemannian) manifolds with an affine connection. $\endgroup$
    – Pedro Lauridsen Ribeiro
    Commented Feb 8, 2021 at 6:48
  • $\begingroup$ I had an undergraduate research student learn differential geometry for his project through that book alone. I don't think there really is a comparable textbook on differential geometry, if you take all of that into account. $\endgroup$
    – Pedro Lauridsen Ribeiro
    Commented Feb 8, 2021 at 6:48
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    $\begingroup$ @PedroLauridsenRibeiro aareyanmanzoor.github.io/assets/hicks.pdf $\endgroup$
    – C.F.G
    Commented Aug 11, 2022 at 4:37
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Curvature and Characteristic classes by J. L. Dupont.

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Structures on manifolds, by Kentaro Yano and Masahiro Kon would be nice.

It is deep, broad, has been influential and as far as i know there is no other edition than the 1984, 1985 editions (which have rather low-quality typesetting).

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Seminar on the Atiyah-Singer Index theorem by Richard Palais

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Both Hejhal's books The Selberg Trace Formula for $\mathrm{PSL}_2(\mathbb R)$ are unique references for the classical version of the trace formula in high generality. It computes all the terms explicitly even for vector valued modular forms, including odd weights and nebentypus, and I cannot think of any other reference superseding it.

Unfortunately, these lecture notes published by Springer LNM are difficult to read: it is a very technical topic, with many one-page long formulas, and all the math is handwritten.

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It's more of a book-length paper than an actual book, but I always wanted a LaTeX version of E. T. Jaynes' where do we stand on maximum entropy?. I retyped about 20% of it myself at some point, but never finished the project.

EDIT 2022-03-16: This has now been typeset here: https://github.com/arxetype/jaynes78

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    $\begingroup$ Perhaps you could make your partial effort available, say, as a git repository, so that others could build on it rather than starting from scratch? $\endgroup$
    – LSpice
    Commented Dec 19, 2018 at 13:57
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    $\begingroup$ @LSpice if anyone seriously wants to continue the project I'd be happy to provide it to them. My version goes up to equation B20, and keeps the layout, numbering and punctuation as close to the original as possible. The references are not done yet. $\endgroup$
    – N. Virgo
    Commented Dec 23, 2018 at 4:51
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    $\begingroup$ The paper has now been typeset. They didn't have permissions to edit this answer so they asked on reddit and I've inserted their link above. $\endgroup$
    – Oscar Cunningham
    Commented Mar 16, 2022 at 13:51
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History of Functional analysis by Jean Dieudonné is a very interesting book, but it is "set" with a typewriter.

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It's slightly prankish but I have to mention Felix Klein's "Riemannsche Flächen: Vorlesungen, gehalten in Göttingen 1891/92" (Riemann surfaces, lectures held in Göttingen 1891/92):

https://archive.org/details/riemannscheflch00purkgoog

The whole book is handwritten! I love looking at the page scans even though I have no idea what they say.

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Grothendieck et al.'s SGA n for n >= 5. SMF has done SGA1,2,4, and SGA3.1 and 3.3, with a draft of 3.2 available online. I think it is difficult to overestimate how relevant these books still are.

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Maybe it would be nice to put in one place pointers to projects aiming to retype old books:

  1. [WIP 10%; me] Adams's blue book [pdf] [source] [notes regarding the re-typesetting];
  2. [Complete (fixing some Tex issues); C.F.G.] Milnor's Morse Theory [link];
  3. [WIP 2%; C.F.G.] Characteristic Classes by Stasheff and Milnor [link];
  4. [WIP 95%; C.F.G.] Milnor's Lectures on the h-cobordism theorem [link];
  5. [0%; C.F.G.] Grothendieck's a general theory of fibre spaces with structure sheaf [link].
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  • $\begingroup$ Are you still doing the Adams book? $\endgroup$
    – C.F.G
    Commented Jul 14, 2021 at 12:45
  • $\begingroup$ @C.F.G the Adams book has been recently been done; see my recent answer. $\endgroup$
    – andres
    Commented Jul 19, 2022 at 23:05
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Local Fields by J. W. S. Cassels. (Maybe even O'Meara's Introduction to Quadratic Forms).

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Dan Henry's "Geometric Theory of Semilinear Parabolic Equations". This 1981 text is (in my opinion) really well written, but can be a chore to read due to the typewriter math. As a runner up in the same category, I'd say Dodd et al., "Solitons and Nonlinear Wave Equations".

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Two collections of papers on category theory from the 70s:

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