This subject aims to introduce an efficient method for solving linear system of ordinary differential equations (ODE). The qualitative theory of ODE will be introduced as well as the study of the phase plane analysis. Linearization of nonlinear system will be carefully Hart man-Grobman theorem studied and local and global stability and unstability as well. Limit sets and limit cycles, Lasalle’s invariance principal, strange attractors and bifurcation theory will be presented. The Poincare-Bendixon theorem and the Liapunov stability theorem will be studied also.