Introduction
1. Poisson-Lie groups and Lie bialgebras
2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation
3. Solutions of the classical Yang-Baxter equation
4. Quasitriangular Hopf algebras
5. Representations and quasitensor categories
6. Quantization of Lie bialgebras
7. Quantized function algebras
8. Structure of QUE algebras: the universal R-matrix
9. Specializations of QUE algebras
10. Representations of QUE algebras: the generic case
11. Representations of QUE algebras: the root of unity case
12. Infinite-dimensional quantum groups
13. Quantum harmonic analysis
14. Canonical bases
15. Quantum group invariants of knots and 3-manifolds
16. Quasi-Hopf algebras and the Knizhnik-Zamolodchikov equation
Appendix. The Kac-Moody algebras.
