Kato K., Kurokawa N., Saito T. Number theory 1. Fermat's dream

Providence: American Mathematical Society, 2000. — 157 p.This is the English translation of the original Japanese book. In this volume, “Fermat's Dream”, core theories in modern number theory are introduced. Developments are given in elliptic curves, pp-adic numbers, the ζζ-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.