The 1992/3 academic year at the Mathematical Sciences Research Institute was devoted to complex algebraic geometry. This 1996 volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. To put it succinctly, algebraic geometry has opened up to ideas and connections from other fields that have traditionally been far away. The editors of the volume, Herbert Clemens and Janos Kollar, chaired the organizing committee. Activities were centered around themes, one per month, under the guidance of experts in each area. There were also four short workshops, which attracted many participants and helped considerably in communicating the new directions in algebraic geometry to a large audience. This book gives a good idea of the intellectual content of the special year and of the workshops.