Table of contents

1. Cover
2. Half-title
3. Series information
4. Frontispiece
5. Title page
6. Copyright information
7. Contents
8. Preface
9. Introduction
10. Conventions and notation
11. 1 Definitions and Basic Properties
12. 2 Examples and Basic Constructions
13. 3 Affine Algebraic Groups and Hopf Algebras
14. 4 Linear Representations of Algebraic Groups
15. 5 Group Theory; the Isomorphism Theorems
16. 6 Subnormal Series; Solvable and Nilpotent Algebraic Groups
17. 7 Algebraic Groups Acting on Schemes
18. 8 The Structure of General Algebraic Groups
19. 9 Tannaka Duality; Jordan Decompositions
20. 10 The Lie Algebra of an Algebraic Group
21. 11 Finite Group Schemes
22. 12 Groups of Multiplicative Type; Linearly Reductive Groups
23. 13 Tori Acting on Schemes
24. 14 Unipotent Algebraic Groups
25. 15 Cohomology and Extensions
26. 16 The Structure of Solvable Algebraic Groups
27. 17 Borel Subgroups and Applications
28. 18 The Geometry of Algebraic Groups
29. 19 Semisimple and Reductive Groups
30. 20 Algebraic Groups of Semisimple Rank One
31. 21 Split Reductive Groups
32. 22 Representations of Reductive Groups
33. 23 The Isogeny and Existence Theorems
34. 24 Construction of the Semisimple Groups
35. 25 Additional Topics
36. 26 Review of Algebraic Geometry
37. 27 Existence of Quotients of Algebraic Groups
38. Appendix C Root Data
39. References
40. Index