This monograph presents the theory of Lyapunov's senior indicators and general indicators of pain for linear nonstationary and close to them nonlinear equations ;. The second method of Lyapunov and its interpretation in spaces with definite and indefinite metrics ; Flocke's theorem and localization theorems on the spectrum of the monodromy operator, decomposition of the operator logarithm into a series; the theory of canonical equations with periodic Hamiltonian, the central zone of tenacity, signs of Lyapunov stability and their various generalizations ; Fuchs-Frobenius theory ; exponential cleavage of solutions of linear nonstationary equations, exponential dichotomy ; the theory of integral manifolds, studies of Bol, Bogolyubov, etc. ; generalization of the asymptotic methods of Birkhoff, Tamarkin, et al.