This book attempts to present the most basic concepts and results of Classical Probability Theory and Stochastic Processes.

Probability Theory, which developed under the need to solve specific problems—initially related to games of chance and later related to many other practical activities and almost all sciences, such as Physics, Biology, Medicine, Economics, etc.—explores the behavior of random phenomena through established laws of randomness.

Here, after establishing the axiomatic foundation of probabilities, one-dimensional and multidimensional distributions are introduced, while the presentation concludes with an introduction to limit theorems.

The Theory of Stochastic Processes can be considered as the dynamic part of Probability Theory. It investigates the evolution of systems over time (sometimes in space), when their functioning is influenced by the factor of chance and which are referred to as stochastic systems.

This is achieved through the development, study, and application of specific mathematical models, which are referred to as Stochastic Processes. Here, an attempt is made to develop the most useful applications of such models, specifically Markov Chains.

The book contains approximately 230 exercises with their solutions, unsolved problems, and is complemented by English terminology, useful for further study of the international literature.

This can be used for teaching two or three semester courses, depending on the mathematical background of the students and the goals of the course. The prerequisites for understanding the book are a basic knowledge of Calculus as well as Set Theory, where the latter is presented in an Appendix.