Abstarct: The present thesis is organized in four sections. In the first section some basic and fundamental concepts of the geometry of manifolds such as vector feilds, tangent spaces, tansors, differential forms, Lie groups and etc. are introduced. Second section is devoted to some Riemannian geometry concepts like connections, geodesics and etc. Infinitesimal invariance, system of differential equations, symmetry and symmetry analysis are mentioned in section three. Finally the main topic of this thesis i.e., the classification of Rindler geodesics are coming in section four.