Table of Contents

Preface * Contributors * Schedule of Lectures * Introduction * An Overview of the Proof of Fermat's Last Theorem * A Survey of the Arithmetic Theory of Elliptic Curves * Modular Curves, Hecke Correspondences, and L-Functions * Galois Cohomology * Finite Flat Group Schemes * Three Lectures on the Modularity of PE.3 and the Langlands Reciprocity Conjecture * Serre's Conjectures * An Introduction to the Deformation Theory of Galois Representations * Explicit Construction of Universal Deformation Rings * Hecke Algebras and the Gorenstein Property * Criteria for Complete Intersections * l-adic Modular Deformations and Wiles's "Main Conjecture" * The Flat Deformation Functor * Hecke Rings and Universal Deformation Rings * Explicit Families of Elliptic Curves with Prescribed Mod N Representations * Modularity of Mod 5 Representations * An Extension of Wiles' Results * Appendix to Chapter 17: Classification of PE.1 by the j Invariant of E * Class Field Theory and the First Case of Fermat's Last Theorem * Remarks on the History of Fermat's Last Theorem 1844 to 1984 * On Ternary Equations of Fermat Type and Relations with Elliptic Curves * Wiles' Theorem and the Arithmetic of Elliptic Curves.