Lectures on the Mordell-Weil Theorem

The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegels and Bakers theorems, Hilberts irreducibility theorem, and the large sieve. Included are applications to, for example, Mordells conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.