An Introduction to Lie Groups, Lie Algebras and their Representation Theory

Abstract

In this thesis, we give an extensive introduction to Lie groups and Lie algebras. We conclude the thesis by providing the basic concept of the finite representation theory of a semisimple lie Algebra. The reader is expected to have some general knowledge of group theory, linear algebra, representation theory and topology. We do not demand the reader to have much prior knowledge of topology, hence we will also devote a great part of this thesis to discussing the preliminary knowledge necessary for Lie theory (e.g. manifolds, tangent spaces, vector fields, and integral curves).