Lectures on the Mordell-Weil Theorem (Paperback, 3rd ed. 1997. Softcover reprint of the original 3rd ed. 1997)

The book is based on a course given by J.-P. Serre at the College 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."