The first textbook on the subgroup structure, in particular maximal subgroups, for both algebraic and finite groups of Lie type.

Preface; List of tables; Notation; Part I. Linear Algebraic Groups: 1. Basic concepts; 2. Jordan decomposition; 3. Commutative linear algebraic groups; 4. Connected solvable groups; 5. G-spaces and quotients; 6. Borel subgroups; 7. The Lie algebra of a linear algebraic group; 8. Structure of reductive groups; 9. The classification of semisimple algebraic groups; 10. Exercises for Part I; Part II. Subgroup Structure and Representation Theory of Semisimple Algebraic Groups: 11. BN-pairs and Bruhat decomposition; 12. Structure of parabolic subgroups, I; 13. Subgroups of maximal rank; 14. Centralizers and conjugacy classes; 15. Representations of algebraic groups; 16. Representation theory and maximal subgroups; 17. Structure of parabolic subgroups, II; 18. Maximal subgroups of classical type simple algebraic groups; 19. Maximal subgroups of exceptional type algebraic groups; 20. Exercises for Part II; Part III. Finite Groups of Lie Type: 21. Steinberg endomorphisms; 22. Classification of finite groups of Lie type; 23. Weyl group, root system and root subgroups; 24. A BN-pair for GF; 25. Tori and Sylow subgroups; 26. Subgroups of maximal rank; 27. Maximal subgroups of finite classical groups; 28. About the classes CF1, ¿, CF7 and S; 29. Exceptional groups of Lie type; 30. Exercises for Part III; Appendix A. Root systems; Appendix B. Subsystems; Appendix C. Automorphisms of root systems; References; Index.

Gunter Malle is a Professor in the Department of Mathematics at the University of Kaiserslautern, Germany.