This project is a conference to be held at Rutgers University in March 1988. The purpose of the research meeting is to explore new approaches to the understanding of the mathematical structure of finite groups. In particular, the focus will involve a clarification and shortening of the proof of the classification theorem of finite simple groups. This classification theorem is approximately 10,000 pages in length. In addition to Foundation funds, Rutgers University will contribute substantial support for this meeting. A group is a fundamental algebraic object in mathematics, physics, and chemistry. The building blocks of finite groups are the finite simple groups.