Lectures on the Mordell-Weil Theorem (1997. Softcover Reprint of the Original 3rd 1997)Paperback - 1997. Softcover Reprint of the Original 3rd 1997, 13 November 2013

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, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.