9700735 Dodziuk In 1983, Daniel Gorenstein announced the completion of a major mathematical undertaking: the Classification of the Finite Simple Groups. In that same year Gorenstein and Richard Lyons of Rutgers University launched a project to write a coherent and largely self-contained proof of the classification theorem. By a combination of new ideas and improved organization the goal was to refine the existing 15,000 pages of journal articles down to a more readable 5,000 page proof. Publication of the series by the American Mathematics Society began in 1994 and two volumes have appeared to date. Recent exciting developments have accelerated the pace of activity in this field. This award supports a conference in which the principal players as well as young researchers can meet and chart the road map for future developments. A group is an algebraic system with a single operation obeying certain laws. Examples of groups are found everywhere in nature and their study has important applications to physics, chemistry , biology and communications. The finite simple groups are the fundamental building blocks of groups.