Introduction to modern number theory. Fundamental problems, ideas and theories. Transl. from the Russian. 2nd revised ed. (English) Zbl 1079.11002

Encyclopaedia of Mathematical Sciences 49. Number Theory 1. Berlin: Springer (ISBN 3-540-20364-8/hbk). xv, 514 p. (2005).
This second edition (514 pages) is very much enlarged with respect to the first edition of 1990 (Zbl 0732.11002) (English translation (1995; Zbl 0848.11001) with 303 pages). The new sections, written for the second edition, include a sketch of Wiles’ proof of Fermat’s Last Theorem, and relevant techniques coming from a synthesis of various theories explained already in the first edition. There is a whole new Part III dedicated to arithmetical cohomology, noncommutative geometry and some other subjects. In this way the authors included in this introduction to modern number theory the important achievements of algebraic number theory since 1990.


11-02 Research exposition (monographs, survey articles) pertaining to number theory
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry