الفهرس 
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Abstract
The differential equations, either ordinary or partial, have many applications in describing nature phenomena in diverse scientific fields particularly in physics such as plasma physics, fluid mechanics, optical fibers, solid state physics and nonlinear optics. Finding exact solutions of differential equations is a big goal to many researchers. Lie symmetry method is an essential tool that helps researchers to obtain exact solutions of differential equations. The objective of this thesis is to apply Lie symmetry method that transforms the ordinary and partial differential equations to reduced equations that can be solved in easier ways. The thesis is arranged in four chapter. Chapter one is an introduction to the concept of symmetry and Lie groups. Also we illustrate how the infinitesimal generators are obtained. Those generators are responsible for the transformation of an ordinary differential equation to another one by using new variables (canonical coordinates). Also those generators are used to reduce the number of independent variables of the partial differential equations by one in each time. In Chapter two,symmetry analysis of (1+1)-dimensional partial differential equations are studied. The problems solved in this chapter include Klein-Gordon equations with three forms, scalar Qiao equation and Korteweg–de Vries equation (KdV) like equations.In Chapter three, symmetry analysis of (2+1)-dimensional partial differential equations are studied. The problems solved in this chapter Kadomtsev–Petviashvili equation with p-power, Boussinesq equation, Kadomtsev-Petviashvili Hierarchy, potential Boiti-Leon-Manna-Pempinelli equation and system of Burgers’ equations.Finally, Chapter four is devoted to present the conclusion and suggested future work of this thesis.