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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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A Course of Modern Analysis by Whittaker and Watson

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    $\begingroup$ I think that one is pretty OK typeset, as is, at least my cooy. (The previous owner of my copy was a smoker, so I have the problem that it stinks. But it is a joy to read anyways.) $\endgroup$
    – mickep
    Commented Dec 23, 2018 at 12:39
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Linear and Quasi-linear Equations of Parabolic Type by O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural′ceva

https://bookstore.ams.org/mmono-23

Linear and Quasilinear Elliptic Equations by Nina Uraltseva and Olga Ladyzhenskaya

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A Discord group was recently created with the goal of re-typesetting some old books. We recently finished the first revision of Adams' Stable homotopy and generalised homology, which is now available on Doug Ravenel's website here.

We are currently doing Hicks' Notes on Differential Geometry. If you are interested in helping out, please join the Discord server through this link: https://discord.gg/2JjKvCqHhG. In addition to writers, we need artists to draw diagrams and proofreaders to make sure the writers and artists aren't messing around.

Proposed future books include:

  • H. Triebel - Interpolation Theory, Function Spaces, Differential Operators;
  • D. Rolfsen - Knots and Links;
  • D. Quillen - Homotopical Algebra;
  • H. Matsumura - Commutative Algebra;
  • D. Quillen - Homology of Commutative Rings.
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I would like a book, written in english typeset in LATEX and updated to modern notation, which includes some abridged form of the Polish journal Fundamenta Mathematicae up until World War II (this amounts to 32 volumes over 20 years).

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They contain incredible amounts of beautiful topology there which is largely inaccessible due to language (mostly French I believe), notation, and occasionally poor typesetting. I feel that their knowledge and perspective is lost to most modern researchers. No book comes close to addressing their contents.

This of course would be a major project, but name your price as far as I'm concerned. It would be the type of book every mathematician should own.

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    $\begingroup$ Back issues of Fundamenta are freely available online. A project such as the one you describe would be rather expensive and not so easily accessible. $\endgroup$
    – Andrés E. Caicedo
    Commented Dec 17, 2018 at 23:09
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    $\begingroup$ @AndrésE.Caicedo Yes, I'm aware. And admittedly if I were better at reading French those originals would probably be fine for me. $\endgroup$
    – Forever Mozart
    Commented Dec 17, 2018 at 23:14
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Hilbert’s Foundations of Geometry, with errata and better diagrams.

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    $\begingroup$ It is already done here. $\endgroup$
    – user57432
    Commented Dec 18, 2018 at 4:01
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Number Fields by Daniel A. Marcus.

That's my favorite candidate for real typesetting for two reasons: the book is great and the typewritten text is awful to look at. And it was so at the time the book came out.

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    $\begingroup$ Oh, this has been done by Springer: springer.com/us/book/9783319902326 $\endgroup$
    – lhf
    Commented Dec 21, 2018 at 1:00
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    $\begingroup$ Good to know! It's nice that they finally made it pleasant to look at. $\endgroup$
    – Not a grad student
    Commented Dec 26, 2018 at 17:38
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Rudin, W., Function theory in polydiscs, Mathematics Lecture Note Series. New York-Amsterdam: W.A. Benjamin, Inc., 188 p. (1969). ZBL0177.34101.

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Differential Geometry in the Large: Seminar Lectures New York University 1946 and Stanford University 1956 by Heinz Hopf.

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Antwerp Proceedings, ie Modular Functions in One Variable from 1972. Important historical testament with numerous classic studies (Deligne-Rapoport on moduli of elliptic curves, Deligne on $L$-function, Swinnerton-Dyer on image of Galois Representation, Serre, and Katz on $p$-adic modular form, Tate's algorithm, BSD conjecture, etc) and the volumes are so big that they can break apart physically upon casual perusal. Typeset on a typewriter unfortunately.

(I own the volumes previous owned by late Swinnerton-Dyer, who probably kept the set on the shelf, but they easily started to develop crevices once I started reading)

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The Homology of Iterated Loop Spaces (Thomas Joseph Lada, J. Peter May, Frederick Ronald Cohen),

The Geometry of Iterated Loop Spaces (J. Peter May), [EDIT: has been done by Nicholas Hamblet, pdf link]

$E_\infty$ ring spaces and $E_\infty$ ring spectra (J. Peter May),

$H_\infty$ ring spectra and their applications (R. R. Bruner, J. Peter May, James McClure),

Equivariant stable homotopy theory (L. Gaunce Lewis, Mark Steinberger, J. Peter May), and

A general algebraic approach to Steenrod operations (J. Peter May) which is not a book but an article essential to most of the mentionned books.

These are books and papers that I would love to have in a beautiful LaTeX version because they have major historical importance, are still important references which are quoted everyday, and present some proofs and computations that have not been fully exposed in one comprehensive reference as far as I know (and the recent documents very often cite these when it comes to technicalities). The article of May would deserve new modern notations also...

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Leonhard Euler's Vollständige Anleitung zur Differenzial-Rechnung and his Vollständige Anleitung zur Integralrechnung.

Edit Dec. 2023: LaTeX'd versions of Euler's Institutiones calculi differentialis can be found for:

  • Vol. 1 on the homepage of the Euler-Kreis Mainz (German translation by A. Aycock)

  • Vol. 2 on arxiv (English translation by A. Aycock)

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  • $\begingroup$ Wow! Did Euler ever publish in German? I thought he published all in Latin. $\endgroup$
    – Allawonder
    Commented Apr 30, 2019 at 17:42
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    $\begingroup$ @Allawonder I'm not aware of a good english translation of this. If there is one that would also be nice. $\endgroup$
    – Michael Bächtold
    Commented May 1, 2019 at 9:14
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    $\begingroup$ Oh, but John D. Blanton has made a translation on the first nine chapters on the one on differentials, published by Springer-Verlag as Foundations of Differential Calculus. It's sad that Blanton doesn't complete the work. However, Ian Bruce has commenced on an ambitious translation project, where he has translated both books completely -- however, I cannot say it reads as nicely as Blanton's translation, but since I'm not able to read Latin I have to do only with what's available. See Bruce's project at 17centurymaths.com $\endgroup$
    – Allawonder
    Commented May 1, 2019 at 9:41
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    $\begingroup$ @Allawonder Thanks! I had forgotten Blanton's translation but was aware of Bruce's. I haven't read much of Bruce's translation, but noticed in one particular case, that it was not of much help. $\endgroup$
    – Michael Bächtold
    Commented May 1, 2019 at 10:06
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    $\begingroup$ I agree with you that Bruce's translation is sometimes difficult to understand. I hinted at something like that in my last comment. However, since there are no others... $\endgroup$
    – Allawonder
    Commented May 1, 2019 at 10:17
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All eight volumes of Grothendieck's Éléments de géométrie algébrique, from 1960-1967.

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    $\begingroup$ What's wrong with the typesetting of these ones? The versions available via Numdam seem fine to me. $\endgroup$
    – Fred Rohrer
    Commented Dec 18, 2018 at 17:56
  • $\begingroup$ @FredRohrer apologies; the only version I had seen before had much worse typesetting $\endgroup$
    – Liam Baker
    Commented Dec 18, 2018 at 18:13
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There are many beautiful mathematical books, e.g. by Milnor, Serre, ... However, if I had to select only one, it would be by Emil Artin, Theory of Algebraic Numbers.

It should be allowed to make some minor editing. Indeed, the book is exceptionally elegant despite the fact that the note taker and translator were not always understanding the text. For instance, a marginal remark was called a theorem when the real result was stated as a regular part of the text. But then, who knows, possibly this is also a part of this charming and profound monography.

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    $\begingroup$ Perhaps this book is included as part of "Expostion by Emil Artin: A Selection", pag. 120-250, published by the AMS. $\endgroup$
    – F Zaldivar
    Commented Dec 20, 2018 at 17:30
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Topics in multiplicative number theory by H.L. Montgomery. It is not out of print, but a version in LaTeX quality would be a significant improvement.

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I don't know whether the book mentioned in the question is readable or not yet; so I post it as an answer:

Curvature and Betti numbers by K. Yano and S. Bochner.

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"Surface Area" by Lamberto Cesari, published by Princeton University press in 1956. It is similar to "Length and Area" of Tibor Rado, but the contents of the two books do not overlap and the book by Cesari has a complete bibliography that covers perhaps all contributions to the area problem from its beginning around 1900 up to its date of publication: also, it includes Cesari's complete solution to this problem, which is not easy to find elsewhere at all, since it was published in several large memories by the "Reale Accademia d'Italia" during the WWII.

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  • $\begingroup$ To the downvoter: what are the reasons for your "thumbs down"? $\endgroup$
    – Daniele Tampieri
    Commented May 29 at 12:28
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Stong, Robert E. (1968). Notes on cobordism theory. Mathematical notes. Princeton, NJ: Princeton University Press.

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  • $\begingroup$ Oh yes please... ! $\endgroup$
    – elidiot
    Commented May 10, 2020 at 19:32
  • $\begingroup$ Unfortunately this answer not highly up-voted!! So I don't think it is useful to do this. $\endgroup$
    – C.F.G
    Commented May 10, 2020 at 20:44
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A preprint of G. Perelman: Alexandrov's space with curvatures bounded from below II.

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Chern S.S. - Complex manifolds without potential theory (With an Appendix on the Geometry of Characteristic Classes)- Springer (1995)

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Not so bad quality but I'd like to see the following recent books in new typesetting:

  1. do Carmo, Manfredo Perdigão, Riemannian geometry. Translated from the Portuguese by Francis Flaherty, Mathematics: Theory & Applications. Boston, MA etc.: Birkhäuser. xiii, 300 p. (1992). ZBL0752.53001.
  2. Helgason, Sigurdur, Differential geometry, Lie groups, and symmetric spaces., Graduate Studies in Mathematics. 34. Providence, RI: American Mathematical Society (AMS). xxvi, 641 p. (2001). ZBL0993.53002.
  3. Guillemin, Victor; Pollack, Alan, Differential topology, Providence, RI: AMS Chelsea Publishing (ISBN 978-0-8218-5193-7/hbk). xviii, 222 p. (2010). ZBL1420.57001.
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  • $\begingroup$ +1 for Helgason's Differential geometry, Lie groups, and symmetric spaces $\endgroup$
    – Onur Oktay
    Commented Aug 12, 2022 at 9:21
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Gekeler's Drinfeld Modular Curves, 1986

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I am very surprised no one has mentioned Sheaf Theory by B.R. Tennison. It is an awesome book : definitions and theorems are stated very precisely yet lucidly, and the proofs are detailed. It is a favorite of many Algebraic Geometers.

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Selected volumes from the Interdisciplinary Mathematics series. written and published by Robert Hermann (1931 - 2020). Good starting points:

Geometric Theory of Non-Linear Differential Equations, Backlund Transformations and Solitons (XII part A and XIV part B)

Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks (XV part A, XVIII part B)

Cartanian Geometry, Nonlinear Waves, and Control Theory (XX part A, XXI part B)

Interesting ideas, some of which remain to be explored. Being privately published and decades old, the books are hard to obtain, too.

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Little & Ives 1958 Complete book of Science

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    $\begingroup$ That book was beautifully typeset (see rubylane.com/item/632271-007689/…). It is not hard to find a copy, and not expensive. Your answer doesn't seem to me to be in the spirit of this question. $\endgroup$
    – Ben McKay
    Commented Dec 18, 2018 at 8:59
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