abstract: The course is an introduction to the theory of Markov processes with general paths. Basic results on stochastic equations, sufficient to construct such processes are covered as well. The course is divided into 6 parts: 1. Markov processes in discrete time, 2. Markovian semigroups and Courrage theorem, 3. Levy processes, 4. Properties of trajectories, 5. Stochastic equations in finite and infinite dimensions. Literature: 1. G. Da Prato and J. Zabczyk, "Stochastic Equations in Infinite Dimensions", CUP, 1992. 2. I. I. Gikhman and A.V. Skorochod, "The Theory of Stochastic Processes", Springer,vol.1-3,1974-75- 79. 3. P. Protter, "Stochastic Integration and Differential Equations", Springer, 2004. 4. D. Stroock, "Markov Processes from Ito's Point of View", Princeton University Press, 2003. 5. J. Zabczyk, "Topics in Stochastic Processes", Quaderni, SNS Pisa, 2004.