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.