Introduction

The colloquium “Elliptic Curves and Modular Forms” was held at the National Academy of Sciences in Washington, DC, March 15–17, 1996. The topics covered by this colloquium have been extraordinarily active lately. These topics have played an essential role in some of the exciting recent work on classical problems, including Fermat’s Last Theorem. They will surely continue to be central to further developments in Number Theory. The 11 articles to follow are the texts of addresses given during this colloquium. These articles range from the study of “p-adic Galois representations, L functions, modular forms, and the p-adic congruences they satisfy” (as in the articles by John Coates, Robert Coleman, Fred Diamond, Jean-Marc Fontaine, Ralph Greenberg, Haruzo Hida, Bernadette Perrin-Riou, and Richard Taylor) to the study of the delicate geometry of modular curves and Shimura varieties (as in the articles by Gerd Faltings and Ken Ribet) to the analytic number-theoretic study of Zeta functions and Eisenstein series of classical groups (as in the article by Goro Shimura).