These proceedings consist of abstracts submitted by participants in the Gainesville Conference on Finite Groups held March 23 and 2'i, 1972, at the University of Florida. It is hoped that these papers will give some indication of the current state of the art of finite group theory. The editors wish to express their appreciation to the University of Florida Department of Mathematics for providing the financial support of this conference. We would also like to thank the North Holland Publishing Company for publishing these proceedings. Finally the editors take this opportunity to thank Mrs. Linda Carver and Mrs. Betty Holley for their valuable assistance in making arrangements for the conference and to thank Mrs. Vicki Shult for careful preparation of the manuscript for publication.