Argthtjtr

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.

Morse Theory by Milnor (and Spivak and Wells)

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.

Just for fun, Principia mathematica.

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.

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 general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck

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.

Borevich-Shafarevich in English or French. Without typos and with modern notation. Please.

Complexe Cotangent et Déformations I & II by Illusie

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 $sqrt{7+4sqrt{3}}$?

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).

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.

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.

Arithmétique des algèbres de quaternions by Marie-France Vigneras

Curvature and Characteristic classes by J. L. Dupont.

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).

All volumes of Asterisque, from 1973 to about 1990.

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

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.

Local Fields by J. W. S. Cassels. (Maybe even O'Meara's Introduction to Quadratic Forms).

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".

Infinite Loop Spaces by John F. Adams and Notes on Crystalline Cohomology by Pierre Berthelot and Arthur Ogus

Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya

Seminar on the Atiyah-Singer Index theorem by Richard Palais

Rudin, W., Function theory in polydiscs, Mathematics Lecture Note Series. New York-Amsterdam: W.A. Benjamin, Inc., 188 p. (1969). ZBL0177.34101.

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.

Hilbert’s Foundations of Geometry, with errata and better diagrams.

All eight volumes of Grothendieck's Éléments de géométrie algébrique, from 1960-1967.

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.

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

• Coherence in categories


• Proceedings of the Sydney Category Theory Seminar

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.