1. Preliminary results; 2. Permutation representations; 3. Representations of groups on groups; 4. Linear representations; 5. Permutation groups; 6. Extensions of groups and modules; 7. Spaces with forms; 8. p-Groups; 9. Change of field of a linear representation; 10. Presentations of groups; 11. The generalized Fitting subgroup; 12. Linear representations of finite groups; 13. Transfer and fusion; 14. The geometry of groups of Lie type; 15. Signalizer functors; 16. Finite simple groups.
The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.
'I consider this book as an extremely valuable source and help for anyone interested in a serious study of finite groups.' U. Dempwolff, Zentralblatt MATH