It is the 3rd edition of the textbook devoted to initial information and basic topics from the theory of stochastic processes. The book consists of six chapters and an appendix, the latter contains a review of probability. Chapter 1, “Markov chains”, contains, in particular, the sections, devoted to stationary distributions, detailed balance condition, exit distributions, exit times and infinite state spaces. In Chapter 2, “Poisson processes”, the reader will find the theory of compound Poisson processes and also description of some transformations including thinning, superpositions and conditioning. Chapter 3, “Renewal processes”, describes respective laws of large numbers, applications to queueing theory and such question as age and residual life. Chapter 4, “Continuous time Markov chains” is devoted to the same questions as Chapter 1 but in application to more complicated objects. It contains also Markovian queues and even Markovian networks. Chapter 5, “Martingales”, describes gambling strategies, stopping times and several applications, in particular, to ruin probabilities and queues. Chapter 6, “Mathematical finance”, contains binomial model, Black-Scholes formula, American options, calls and puts. The book is very useful for anyone who is interested in probability theory and its ramifications and applications. It can be recommended both for students and postgraduates, teachers and practitioners. The mathematical level is rigorous but accessible for those who know the preliminaries of probability. The book contains a lot of examples which contribute to a better understanding of the text.