Lie groups Lie algebras and representations : an elementary introduction Part I: General theory Martix Lie groups The matrix exponential Lie algebras Basic representation theory The Baker Campbell Hausdorff formula and its consequences Part II: Semisimple Lie algebras The represantations of sl(3;C) Semisimple Lie algebras Root systems Representations of semisimple Lie algebras Further properties of the representations Part III: Compact Lie groups Compact Lie groups and maximal tori The compact group approach to representation theory Fundamental groups of compact Lie groups A: Linear algebra review B: Differential forms C: Clebsch Gordan theory and the Wigner Eckart theorem D: Completeness of characters