Abstarct: In this thesis, we first introduce the partial differential Equations of the first and second orders; then we express differential transform method for linear and nonlinear functions. We show the efficiency of the proposed method by several numerical examples. Finally, the Fokker-Plank Equation, the Zakharov- Kuznetsov equation and Kuramoto-Sivashinsky equation are solved by the differential transform method. the Fornberg-Whitham equation is also solved by the Reduced differential transform method.