Algebraic groups. The theory of group schemes of finite type over a field

Content: Introduction
 1. Definitions and basic properties
 2. Examples and basic constructions
 3. Affine algebraic groups and Hopf algebras
 4. Linear representations of algebraic groups
 5. Group theory: the isomorphism theorems
 6. Subnormal series: solvable and nilpotent algebraic groups
 7. Algebraic groups acting on schemes
 8. The structure of general algebraic groups
 9. Tannaka duality: Jordan decompositions
 10. The Lie algebra of an algebraic group
 11. Finite group schemes
 12. Groups of multiplicative type: linearly reductive groups
 13. Tori acting on schemes
 14. Unipotent algebraic groups
 15. Cohomology and extensions
 16. The structure of solvable algebraic groups
 17. Borel subgroups and applications
 18. The geometry of algebraic groups
 19. Semisimple and reductive groups
 20. Algebraic groups of semisimple rank one
 21. Split reductive groups
 22. Representations of reductive groups
 23. The isogeny and existence theorems
 24. Construction of the semisimple groups
 25. Additional topics
 Appendix A. Review of algebraic geometry
 Appendix B. Existence of quotients of algebraic groups
 Appendix C. Root data
 Bibliography
 Index.