Old books you would like to have reprinted with high-quality typesetting There are some questions on mathoverflow such as

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*What out-of-print books would you like to see re-printed?

*Old books still used
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:

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


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


*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).
 A: 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
A: Seminar on the Atiyah-Singer Index theorem by Richard Palais
A: History of Functional analysis by Jean Dieudonné is a very interesting book, but it is "set" with a typewriter.
A: 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.
A: 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.
A: Maybe it would be nice to put in one place pointers to projects aiming to retype old books:


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*[WIP 10%; me] Adams's blue book [pdf] [source] [notes regarding the re-typesetting];

*[Complete (fixing some Tex issues); C.F.G.] Milnor's Morse Theory [link];

*[WIP 2%; C.F.G.] Characteristic Classes by Stasheff and Milnor [link];

*[WIP 95%; C.F.G.] Milnor's Lectures on the h-cobordism theorem [link];

*[0%; C.F.G.] Grothendieck's a general theory of fibre spaces with structure sheaf [link].

A: 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".
A: A Course of Modern Analysis by Whittaker and Watson
A: 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
A: Morse Theory by Milnor (and Spivak and Wells)

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

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.
A: Local Fields by J. W. S. Cassels. (Maybe even O'Meara's Introduction to Quadratic Forms). 
A: 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.
A: 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.
A: Hilbert’s Foundations of Geometry, with errata and better diagrams.
A: Two collections of papers on category theory from the 70s:


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*Coherence in categories

*Proceedings of the Sydney Category Theory Seminar
A: 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. 
A: 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:

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*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.

A: 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
A: Rudin, W., Function theory in polydiscs, Mathematics Lecture Note Series. New York-Amsterdam: W.A. Benjamin, Inc., 188 p. (1969). ZBL0177.34101.
A: Leonhard Euler's Vollständige Anleitung zur Differenzial-Rechnung and his
Vollständige Anleitung zur Integralrechnung.
A: Differential Geometry in the Large: Seminar Lectures New York University 1946 and Stanford University 1956 by Heinz Hopf.
A: All eight volumes of Grothendieck's Éléments de géométrie algébrique, from 1960-1967.
A: 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.
A: 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.
A: 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.
A: "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.
A: Stong, Robert E. (1968). Notes on cobordism theory. Mathematical notes. Princeton, NJ: Princeton University Press.
A: 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.
A: Just for fun, Principia mathematica.
A: 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.
A: 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.
A: Complexe Cotangent et Déformations I & II by Illusie
A: Chern S.S. - Complex manifolds without potential theory (With an Appendix on the Geometry of Characteristic Classes)- Springer (1995)
A: 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) 
A: 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...
A: A general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck
A: 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).
A: Borevich-Shafarevich in English or French. Without typos and with modern notation. Please.
A: 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.
A: All volumes of Asterisque, from 1973 to about 1990.
A: 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.
A: Arithmétique des algèbres de quaternions by Marie-France Vigneras
A: Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya
A: 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

*

*$\color{blue}{\text{Has been done! By  TEXromancers group.}}$ Read/Download it here})

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!
A: Curvature and Characteristic classes by J. L. Dupont.
A: 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). 
A: 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.
A: Gekeler's Drinfeld Modular Curves, 1986
A: 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.
A: A preprint of G. Perelman:  Alexandrov's space with curvatures bounded from below II.
A: Not so bad quality but I'd like to see the following recent books in new typesetting:

*

*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.

*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.

*Guillemin, Victor; Pollack, Alan, Differential topology, Providence, RI: AMS Chelsea Publishing (ISBN 978-0-8218-5193-7/hbk). xviii, 222 p. (2010). ZBL1420.57001.

A: 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.
A: Little & Ives 1958 Complete book of Science
