that every elliptic curve over Q is modular. The final difficulties in the proof of the conjectural upper bound for the order of the Selmer group attached to the symmetric square of a modular form, have since been overcome by Wiles with the assistance of R. Taylor. The proof that every semi-stable elliptic curve over Q is modular is not only significant in the study of elliptic curves, but also due to the earlier work of Frey, Ribet, and others, completes a proof of Fermat's last theorem. New paperback re-issue of the revised second edition. CONTENTS Foreword by John Coates and Shing-Tung Yau Fermat's Last Theorem (by H. Darmon, F. Diamond, R. Taylor) Characteristic distributions for non-torsion Lamda-modules (by P. Balister) On the symmetric square of a modular elliptic curve (by J. Coates, A. Sydenham) The refined conjecture of Serre (by Fred Diamond) Wiles minus epsilon implies Fermat (by Norm Elkies) Geometric Galois representations (by J.M. Fontaine, B. Mazur) On elliptic curves (by Gerhard Frey ) Complete intersections and Gorenstein rings (by H.W. Lenstra, Jr.) Homologic des courbes modulaires (by L. Merel) Irreducible Galois representation (by Kenneth A. Ribet) Mod p representations of elliptic curves (by K. Rubin, A. Silverberg) A review of non-Archimedean elliptic functions (by John Tate) On Galois representations associated to Hilbert modular forms II (by Richard Taylor)

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