Abstarct: In this thesis we try to express a general method for finding the solutions of differential equations by using the non-linear superposition principle and the Wei-Norman method and their usage in differential equations. In Chapter 1, we explain the concepts and basic definitions that are needed. In chapter 2, first we state the definitions of prolongation and then the prolongation of vector fields and group action are described with some examples. Other sections of this chapter include differential invariants definition and some methods for calculating. In chapter 3,we review the problem of reducing a second order linear differential equation to a non-linear Riccati differential equation. In the other sections of this chapter we explain a method developed by Wei and Norman for determining the solutions of a differential equations and we apply the method to study Riccati differential equation. The superposition principle for first order differential equations system is studied in chapter 4.