||Though elated at the successful completion of the classification of finite simple groups in the early 1980's, Danny Gorenstein nevertheless immediately appreciated the urgency of a "revision" project, to which he turned without delay. Before long we had joined him in this effort, which is now into its second decade. Danny always kept the project driving forward with relentless energy, contagious optimism and his unique global vision of finite simple group theory. He inspired other collaborators— Richard Foote and Gemot Stroth—to contribute theorems designed to fit our revised strategy. Their work forms a vital part of this project. The conception of these volumes is unmistakably Danny's, and those who know his mathematics and his persuasive way of explaining it should recognize them everywhere. Since his death in 1992, we have tried to maintain his standards and we hope that whatever changes and additions we have made keep the vigorous spirit which was his trademark. Of course the responsibility for any stumbling or errors must remain with us. To accompany him on this mathematical journey was a privilege and as we continue, our debt to our teacher, colleague and loyal friend is hard to measure. Thanks, Danny.
This monograph is Number 1 of a projected dozen or so volumes, and contains two of the roughly thirty chapters which will comprise the entire project. Not all of the chapters are completely written at this juncture, but we anticipate that the publication process, now begun, will continue at a steady pace. In the first section of Chapter 1, we discuss the current status of the work in some more detail; later in that chapter we delineate the background results which form the foundation for all the mathematics in the subsequent volumes.
When Danny began, there was already a well-established tradition of "revisionism" in finite group theory. Indeed, beginning in the late 1960's, Helmut Bender produced a series of "revisions" whose beauty and depth profoundly influenced finite group theory. During the final decade of the classification proof, several more group-theorists showed how to develop deep mathematics while re-addressing some of the fundamental theorems in the theory of simple groups. While it is sometimes difficult to draw a distinct line between revisionist and other mathematics, the clear successes of Bender, Michel Enguehard, George Glauberman, Koichiro Harada, Thomas Peterfalvi, and Bernd Stellmacher in various revisionist projects have inspired us.