In this chapter, we define the Lyapunov stability and give Lyapunov’s theorems. We formulate Lagrange, Lyapunov and Chetaev’s theorems on the stability. Thompson and Tait’s theorems is discussed. Routh–Hurwitz’s and Mikhailov’s criteria are given. The stability of periodicmotions of nonautonomous systems is studied from the linear approximation. The stability of the zero solution of the Mathieu equation is considered, to which one may reduce oscillations of a pendulum with vibrating suspension point.