A guide to quantum groups

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.