Abstract

We will present a few types of algebras which are to-day playing an essential role in physics (especially in elementary particle physics and statistical mechanics). We will
consider three main families of such symmetry algebras, each showing up as a generalisation of the Cartan simple Lie algebras:
1- Simple Lie Superalgebras.
2- Kac-Moody Algebras. 3-Quantum Algebras.

We plan to devote one lecture to each of these three subjects, providing with definitions, classification, main properties on the structure and of the representations of these algebras, as well as some physical applications. We will feel free; to suppress or limit; one of these three items in case it looks more reasonable to develop in more detail another part.