Lie Algebras of Finite and Affine Type

1. Basic concepts 2. Representations of soluble and nilpotent Lie algebras 3. Cartan subalgebras 4. The Cartan decomposition 5. The root systems and the Weyl group 6. The Cartan matrix and the Dynkin diagram 7. The existence and uniqueness theorems 8. The simple Lie algebras 9. Some universal constructions 10. Irreducible modules for semisimple Lie algebras 11. Further properties of the universal enveloping algebra 12. Character and dimension formulae 13. Fundamental modules for simple Lie algebras 14. Generalized Cartan matrices and Kac-Moody algebras 15. The classification of generalised Cartan matrices 16 The invariant form, root system and Weyl group 17. Kac-Moody algebras of affine type 18. Realisations of affine Kac-Moody algebras 19. Some representations of symmetrisable Kac-Moody algebras 20. Representations of affine Kac-Moody algebras 21. Borcherds Lie algebras Appendix.