Ismail Mustafa Mohammed Othman2018-10-082018-10-082016http://hdl.handle.net/123456789/13097A Thesis Submitted in Fulfillment of the requirements for the degree philosophy in MathematicsAbstract _ In this research we studied Lie groups and Lie algebras . We considered the classification theory of complex and semi-simple Lie algebras , provided with sufficient knowledge of the properties of Lie algebras . We then concentrated on the application of Lie algebra to the conservation laws , in particular Noether theorem . We also studied the application of Lie algebra to particle physics including the utility of the representation theory of the five dimensional special unitary group. We concluded our research program with the study of symmetry groups of differential equations.enTheory LieThesis