---

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.

---

Contents: Heights - Nomalized heights - The Mordell-Weil theorem - Mordell´s conjecture - Local calculation of normalized heights - Siegel´s method - Baker´s method - Hilbert´s irreducibility theorem - Construction of Galois extensions - Construction of elliptic curves of large rank - The large sieve - Applications of the large sieve to thin sets.

---

Professor Jean-Pierre Serre ist ein renommierter französischer Mathematiker am Collège de France, Paris.

---