Stochastic stability of differential equations 1. Boundedness in probability and stability of stochastic processes defined by differential equations 2. Stationary and periodic solutions of differential equations 3. Markov processes and stochastic differential equations 4. Ergodic properties of solutions of stochastic equations 5. Stability of stochastic differential equations 6. Systems of linear stochastic equations 7. Some special problems in the theory of stability of SDEs 8. Stabilization of controlled stochastic systems (this chapter was written jointly with M.B. Nevelson) A. Appendix to the first English edition B. Appendix to the second edition: moment Lyapunov exponents and stability index (written jointly with G.N. Milstein)