The main purpose of this book is to: (i) give a systematic introduction to Probability Theory and Stochastic Processes, (ii) present an outline of possible applications of these theories, accompanied by descriptive concrete examples, and (iii) to provide extensive (however, not exhaustive) references of other books in these areas, thereby giving the reader opportunity to complete his/her knowledge of the subjects considered. The material in the text proceeds from simple set theory, simple random experiments, concepts of probability and probability distributions, functions of random variables, and generating functions to simple stochastic processes, in what the authors regard as the logical approach to Probability Theory and Stochastic Processes