1. Basic definitions -- 2. The invariant bilinear form and the generalized Casimir operator -- 3. Integrable representations and the Weyl group of a Kac-Moody algebra -- 4. Some properties of generalized Cartan matrices -- 5. Real and imaginary roots -- 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group -- 7. Affine Lie algebras: the realization (case k = 1) -- 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms -- 9. Highest weight modules over the Lie algebra g(A) -- 10. Integrable highest weight modules: the character formula -- 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem -- 12. Integrable highest weight modules over affine Lie algebras. Application to ?-function identities -- 13. Affine Lie algebras, theta functions and modular forms -- 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations -- Index of notations and definitions -- References