Abstarct: The main purpuse of the present PhD thesis is the geometric study of the application of Lie groups in differential equations and conservation laws comprehsively. The thesis contains six separated sections. After introduction, In the second section, basic and fundamental concepts including transformation, Lie symmetries, and solutions of differential equations are given. Third section is devoted for the study of conservation laws and their methods of calculations. Symmetries and conservation laws for perturbed system are studied in section four. All discussed methods and concepts are generalized for fractional differential equations in section five. Finally some computational packages and codes are introduced in section 6.