The classification of the finite simple groups is one of
the major feats of contemporary mathematical research, but its proof
has never been completely extricated from the journal literature in
which it first appeared. This book serves as an introduction to a
series devoted to organizing and simplifying the proof. The purpose of
the series is to present as direct and coherent a proof as is
possible with existing techniques. This first volume, which sets up
the structure for the entire series, begins with largely
informal discussions of the relationship between the Classification
Theorem and the general structure of finite groups, as well as the
general strategy to be followed in the series and a comparison with
the original proof. Also listed are background results from the
literature that will be used in subsequent volumes. Next, the authors
formally present the structure of the proof and the plan for the series
of volumes in the form of two grids, giving the main case division of
the proof as well as the principal milestones in the analysis of
each case. Thumbnail sketches are given of the ten or so principal
methods underlying the proof. Much of the book is written in an
expository style accessible to nonspecialists.
Readership
The material here ranges from exposition suitable to
a first- or second-year graduate student to more technical
portions suitable for specialists.