This book presents an introduction to stochastic processes. It includes material on Markov chains in discrete and continuous time, martingales and diffusion processes. The mathematical tools are reduced so that there is no need for measure theory in the explanations. Therefore the text is suitable also for non-mathematicians, e.g. engineers, economists, and students and researchers from applied sciences. The main aim is to give ideas and applications of probabilistic models, not always with full proofs of statements and theorems. There are easy exercises at the end of each section and more challenging problems at the end of chapters. In this manner, advanced topics are also investigated, such as the reversibility of Markov chains, the Wiener process and functions of it, martingale methods and an introduction to stochastic calculus (including the Itô formula). Applications of Poisson and branching processes, renewals, birth-death processes and queues, ruin probability, the stock price model, etc., are used to demonstrate the use of various models. The textbook may serve as an undergraduate course for students with a mathematical background in various types of schools.