Lie Algebras of Finite and Affine TypeLie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan Killing Weyl theory of finite dimensional simple algebras and the more modern theory of Kac Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The Appendix provides a summary of the basic properties