Contents. Introduction. 1. Essentials of probability theory and mathematical statistics. 2. Martingales and semimartingales: discrete time. 3. Martingales and semimartingales: continuous time. 4. The Wiener process, the stochastic integral over the Wiener process, and the stochastic differential equations. 5. Square integrable martingales, and structure of the functionals ofa Wiener process. 6. Nonnegatice supermartingales and martingales, and the Girsanov theorem. 7. Absolute continuty of measure corresponding to the Ito processes and process of the diffusion type. 8. General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes. 9. Optimal filtering, interpolation and extrapolation of Markov processes with a counta ble number of state. 10. Optimal linear nonstationary filtering.