This edition has been called startlingly up-to-date, and in this
corrected second printing you can be sure that it 's even more
contemporaneous. It surveys from a unified point of view both the
modern state and the trends of continuing development in various
branches of number theory. Illuminated by elementary problems, the
central ideas of modern theories are laid bare. Some topics covered
include non-Abelian generalizations of class field theory,
recursive computability and Diophantine equations, zeta- and
L-functions. 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.
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