This book presents an introduction to stochastic processes. It covers background for point processes, Markov chains in discrete and continuous time, Brownian motion, and a small section on martingales. The presentation is suitable for students and researchers in the applied sciences and engineering because a knowledge of measure theory is not assumed. On the other hand, the text pays a lot of attention to applications in science, finance, engineering, operations research and computer science. Omitting a number of proofs, it is not a full university mathematical text but its strength is in a development of thinking towards a solution of real-life problems of random nature. Applied topics like queuing models and networks, actuarial risk analysis and maintenance, and many exercises formulated in a variety of practical situations, help the reader to understand the usefulness of probabilistic models of temporal processes. Solutions to most of the exercises are provided in the appendix. The book is highly recommended to students of technical and economical schools.