This volume contains many of the lectures delivered at the AMS Summer Research Institute on Algebraic Geometry held at the University of California, Santa Cruz in July 1995. The aim of the conference was to provide a comprehensive view of the development of algebraic geometry in the past decade and to lay special emphasis on emerging new directions. The focus of the papers in these volumes is on expository surveys of important areas rather than on technical presentations of new results. These proceedings will be an indispensable reference and guide for researchers in algebraic geometry or nearby fields. Features: Comprehensive coverage of developments over the past decade. Emphasis on new directions and future developments. Connections to related fields. Many expository survey papers.