Symmetries, Lie Algebras and RepresentationsThis is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop