Elliptic Curves

This book is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research.; The first part, which grew out of Tate's Haverford lectures, covers the elementary arithmetic theory of elliptic curves over the rationals.; The next two chapters recast the arguments used in the proof of the Mordell theorem into the context of Galois cohomology and descent theory.; This is followed by three chapters on the analytic theory of elliptic curves, including such topics as elliptic functions, theta functions, and modular functions.; Next, the theory of endomorphisms and elliptic curves over infinite and local fields are discussed.; The book concludes with three chapters surveying recent results in the arithmetic theory, especially those related to the conjecture of the Birch and Swinnerton-Dyer.; This new edition contains three new chapters and the addition of two appendices by Stefan Theisen and Otto Forster.; Dale Husemoller is a member of the faculty at the Max Planck Institute of Mathematics.