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I have recently been told of a proposal to produce an English translation of Landau's Handbuch der Lehre von der Verteilung der Primzahlen, and this prompts me to ask a more general question:

Which foreign-language books would you most like to see translated into English?

These could be classics of historical interest, books you would like your students to read, books you would like to teach from, or books of use in your own research.

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    $\begingroup$ The Russian translation of Milnor's Morse Theory. That's a nice book. :) $\endgroup$
    – Ryan Budney
    Commented Mar 11, 2010 at 0:04
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    $\begingroup$ I have both the original and the Russian translation. They're not quite the same -- the translation (that I have anyhow) has more examples and figures. $\endgroup$
    – Ryan Budney
    Commented Mar 11, 2010 at 0:24
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    $\begingroup$ I also have both of them! And I've just check (fast checking) that pictures are absolutely same. Russian version contains small attachments (by Anosov), but they are not... as good as the book and really short, few pages. You know, translation should be a translation (I am sure Arnol'd could add smth interesting to Milnor, I am a student of V.I., but it is not the case). $\endgroup$
    – Petya
    Commented Mar 11, 2010 at 0:36
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    $\begingroup$ At least I understood a meaning of your smile! $\endgroup$
    – Petya
    Commented Mar 11, 2010 at 0:49
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    $\begingroup$ Another interesting question along these lines: which books "lose" the most in translation? I can't read Russian, but apparently Kostrikin's "Around Burnside" is like that. $\endgroup$
    – Steve D
    Commented Mar 11, 2010 at 2:32

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The Collected Work of Carl Ludwig Siegel.

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    $\begingroup$ This is a duplicate; see Zavosh's answer. $\endgroup$
    – Qiaochu Yuan
    Commented Mar 19, 2010 at 7:42
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Over de Grondslagen der Wiskunde , L.E.J Brouwer, his thesis (in Dutch) on the foundations of mathematics.

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  • $\begingroup$ Also Brouwer's other work in Dutch and German. $\endgroup$
    – Paul Taylor
    Commented May 21, 2014 at 18:28
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Catégories et structures by Charrles Ehresmann

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Two volume introduction to Complex Analysis by B.V.Shabat. Actually, I have already translated about 150 pages of the first volume which is about as much as one can cover in Complex Variable undergraduate course offered by a typical U.S. university. I did give the translation as a hand out to my students last year when I taught Complex variables class. I did translation out of frustration with the book of Churchill and Brown.

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There are two books on popular mathematics by Polish mathematicans Krzysztof Ciesielski and Zdzisław Pogoda (both from the Jagiellonian University in Krakow): the first one is Diamenty matematyki [Mathematical diamonds] (cover http://merlin.pl/images_big/3/83-7337-932-0.jpg), the second is Bezmiar matematycznej wyobraźni [The endlessness of mathematical imagination] (I could not find a better transaltion). Both aim at non-specialist, mostly high-school students, and are written in a unique, informal yet rigorous style. Both are very popular and out of print in Poland. A modified version of a chapter in Mathematical diamonds has been translated by Abe Shenitzer and was published in the American Mathematical Monthly as On Ordering the Natural Numbers, or, The Sharkovski Theorem in Vol. 115, No. 2 (Feb., 2008), pp. 159-165.

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  • $\begingroup$ I'd say that Diamenty matematyki should read The diamonds of mathematics. $\endgroup$
    – Tomasz Kania
    Commented Feb 12, 2014 at 15:45
  • $\begingroup$ In their Monthly article mentioned above Ciesielski and Pogoda translate Diamenty matematyki as Mathematical Diamonds in the reference lists. $\endgroup$
    – Dominik Kwietniak
    Commented Feb 12, 2014 at 16:03
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Probably most of the works from Oskar Perron. It has been mentioned already Die Lehre von den Kettenbrüchen, both volumes, but we could also ask for Irrationalzahlen or any of the other works from Perron. Also worth being mentioned, for applied mathematicians, are the works of Grigory Isaakovich Barenblatt, previous to 1994; this is because Barenblatt has consistently worked about scaling phenomena, but from about the beginnings of the 1990's he began to do it on his own, whereas earlier work includes the participation of other marvelous mathematicians, like Z'eldovich; or even works on his own, but it is interesting to compare the evolution of his ideas. So, the name of books with his participation previous to the 1990's, and to my knowledge, not translated into English: * Ja, B Zeldovich, G. I. Barenblatt, V. B. Librovich, G. M. Maxvikadze "Matematicheskaja teorija gorenija i vsriva", 1980 * G. I. Barenblatt, "Podobie, avtomodelnoct, promezhutochnaja asimptotika: teorija i prilozhenija k geofizicheskoi gidrodinamike", 1982 * A. P. Licitsin, G. I. Barenblatt "gidrodinamika i osadkoobrasovanie", 1983 * G. I. Barenblatt, V. N. Entov, V. M. Rizhik, "Dvizhenie zhidkocteii i gazov v prirodnix plactax" 1984 * G. I. Barenblatt, "Analiz razmernosteii" . Uch. pos. M.: MFTI, 1987. 168 с. (I think this last work made it to English under the translation as "Dimensional Analysis", but in that case I saw it only once, at the library of the Department of Applied Mathematics and Theoretical Physics -DAMTP-of Cambridge, UK, many years ago and is likely out of print anyway, plus the edition, to my knowledge was not revised; on top of that, DAMTP changed from Silver Street to Wilberforce road, and I have no idea if that book survived the moving, if indeed was at that library).

Notice also, that in the Nachlass (the collection of manuscripts, left after the death of an academician, and of course in particular a mathematician) of people like Bernhard Riemann or Ernst Zermelo, there might be still some untranslated documents, but then again they also need to be interpreted in a way that could be meaningful, and this because they are not finished, published or even unpublished works, but sketches of something not fully developed.

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Geometrie der Gewebe by W. Blaschke, and G. Bol

Geradenkonfigurationen und algebraische Flächen by G. Barthel, F. Hirzebruch, and T. Höfer

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Chirurgie des grassmanniennes by Laurent Lafforgue.

http://www.ihes.fr/~lafforgue/math/M02-45.pdf

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    $\begingroup$ That sounds so much cooler in French. $\endgroup$
    – Pete L. Clark
    Commented Mar 11, 2010 at 7:22
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O. Perron - Die Lehre von den Kettenbruechen (Band 1-2)

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Riemannsche Geometrie Im Grossen by Gromoll, Klingenberg and Meyer. I remember this book being cited by Gromov in his famous green book for further details about connections.

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Hilbert's collected works are not fully translated into English. E.g. his paper Ueber ternaere definite Formen". Acta Math., 17 (1893), 169–197 was only translated into Russian.

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Bourbaki "Théories spectrales Ch 1-2". This also related to the MO question here.

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Etienne Ghys, Pierre de la Harpe, "Sur les Groupes Hyperboliques d’après Mikhael Gromov"

A detailed exposition of Gromov's ideas, outlined in his "Hyperbolic groups" article.

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I would really love a translation of the third russian edition of "Number Theory" by Borevich and Shafarevich. It has updated notation, revised errata and has numerous new remarks and updated bibliography. Also, the AP english translation is full of misprints. Anyone knows if there is a project of translating this beatiful book?

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I hope I did not miss that in one of the previous answers, but a book worthy of an English translation is "Théorie des distributions" by Laurent Schwartz. The later edition combined Vol I and II as a single book. One could also consider translating Vol III and IV which are his two long papers on vector-valued distributions. About the latter, see this related MO question: English translation of Schwartz's papers on vector-valued distributions

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Friedrich Levi, Geometrische Konfigurationen

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Hilbert-Bernays's "Foundations of Mathematics", it's a shame that this classic work haven't translated yet!

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"Introduction aux groupes arithmétiques" by Armand Borel.

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I'd love to see Weil's book on Kahler geometry: Introduction à l'étude des variétés kählériennes.

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Egbert Brieskorn’s Lineare Algebra und analytische Geometrie - the best textbook on the topic in my POV.

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I haven't read the following, I want to read it just because in his books, Milnor referred to it for some proofs.

Cerf, J., Sur les difféomorphismes de la sphère de dimension trois ($\Gamma_ 4 = 0$), Lecture Notes in Mathematics. 53. Berlin-Heidelberg-New York: Springer-Verlag. XII, 133 p. (1968). ZBL0164.24502.

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Re: For publication of EGA and SGA, see this: http://www.grothendieckcircle.org/

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Teubner-Taschenbuch der Mathematik Teil II

The first part (Teil I) of this book was translated into English as the Oxford User's Guide to Mathematics

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Einfuhrung in die Algebraische Geometrie-B.L. van der WAERDEN

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Durer's works on proportion, which take a Euclidean approach to constructing visible objects.

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    $\begingroup$ Do you mean his Underweysung der Messung mit dem Zirckel und Richtscheyt (Instruction in Measurement with Compass and Straightedge)? $\endgroup$
    – Phil Harmsworth
    Commented Jul 9, 2017 at 3:37
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Paul Gordan ``Vorlesungen ueber Invariantentheorie" available here , both volumes. This is most worthwhile since the content of most other classics is well accounted for in modern texts whereas this way of doing algebraic geometry has been completely forgotten. Poor knowledge of Gordan's methods is a net loss for contemporary mathematics.

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"Quadratische Formen" by Martin Kneser.

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Arithmetique des algebres de quaternions http://www.springer.com/kr/book/9783540099833

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F. Prus-Wisniowski - Szeregi Rzeczywiste (Poland, Uniwersytet Szczecinski) - a monograph on real series. It can be read by first-year students while supplying the reader with very powerful tools for real (and sometimes complex) series; it might surprise the PhD reader. More importantly, it builds a good understanding of the way real series work. Publisher's website

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  • $\begingroup$ I happen to know Prus-Wisniowski personally, and he is a fluent English speaker who also translated several Russian papers for me in the mid 1990s. You might want to consider asking him about this. I suspect a translation would fit nicely into one of the MAA book series. $\endgroup$
    – Dave L Renfro
    Commented Jul 7, 2017 at 14:33
  • $\begingroup$ Dave, what is the MAA book series? :) $\endgroup$
    – cheater
    Commented Jul 7, 2017 at 19:14
  • $\begingroup$ I wasn't thinking of a specific book series, but since you asked, Classroom Resource Materials seems to be a good fit for the book. For example, the widely cited (on Math StackExchange) book Real Infinite Series is in this book series. $\endgroup$
    – Dave L Renfro
    Commented Jul 7, 2017 at 19:36
  • $\begingroup$ What is MAA though? $\endgroup$
    – cheater
    Commented Jul 8, 2017 at 11:22
  • $\begingroup$ MAA = Mathematical Association of America, which is mostly teaching and non-research oriented, in contrast to AMS = American Mathematical Society. $\endgroup$
    – Dave L Renfro
    Commented Jul 10, 2017 at 14:35
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