In this project, we discussed stability, where the stability of the state trajectory or equilibrium state is examined, stability is applied to obtain the behavior of systems of first-order ordinary differential equation and we present two techniques for examining stability: (1) Lyapunov functions, (2) finding the eigenvalues for fundamental matrix. Stability was proposed in 1892 by Russian mathematician A.M.Lyapunov. It is examined with some examples which are presented to show the effectiveness of it for linear and nonlinear systems and also for any higher order differential equation by reducing it into a system of the first order.