Hiba NasrEldin Mohamed2023-03-162023-03-1616http://hdl.handle.net/123456789/19015A thesis Submitted in partial fulfillment for the Degree of Master of Science in MathematicThis research aims to study the representation theory as a tool that transform abstract groups to groups of linear transformations easy to deal with. This research depends on groups and fields theory and vector spaces to construct the structure of these spaces. We studied vector spaces because of structures. In particular we dealt with finite groups and we gave some applications.enGroup Theory and GeneralizationsGroup theoryAlgebraMathematicsThesis