Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories, Edition 2

This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.

From the reviews of the 2nd edition:

"... For my part, I come to praise this fine volume. This book is a highly instructive read ... the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly up-to-date ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007)