This textbook covers several topics from stochastic processes that are based on the concept of Markov processes. Markov processes are stochastic processes for which the prediction of random behavior in the future depends only on the current position. The central concepts of Markov processes are clearly explained and motivated with examples. The text then discusses Brownian motion, stochastic integrals, and stochastic differential equations, providing a detailed description of the fundamental Ito formula. One of the classical applications of stochastic differential equations is Monte Carlo methods for solving partial differential equations. In the last two chapters, some of the basic concepts of financial mathematics are introduced, and it is shown how to apply methods of stochastic differential equations.