Author Description

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. By Victor G. Kac.