The aim of this thesis is to study the stability of the nonlinear systems with stochastic noise and investigate the qualitative properties of it. Principally, we are concerned with stability in probability, almost surly stable and moment exponential stability in the sense of Lyapunov method. Next, we analyze the stability of the stochastic systems by notion of homogeneity. Moreover, based on homogenous results, we present the stabilization method by using homogeneous feedback control. To sum up, this study surveys some stability criteria of the stochastic systems by using Lyapunov method. Also, it is intended to establish sufficient conditions of stabilization of the homogeneous stochastic systems.