This book presents the fundamentals of probability theory, the mathematical science that deals with the laws of random phenomena. These laws play an extremely important role in physical and other fields of natural science, in technology and engineering, economics, linguistics and so forth.

The material covered ranges over the following problems: the concept of probability, sequences of independent trials, Markov chains, random variables and distribution functions, numerical characteristics of random variables, the law of large numbers, characteristic functions, the classical limit theorem, the theory of infinitely divisible distribution laws, the theory of stochastic processes, and elements of the theory of queues.

The theory of probability is presented as a mathematical discipline, however the examples given not only illustrate the general propositions of the theory but provide links with problems that occur in the natural sciences.

This is a text for students of mathematical departments of colleges and universities. It will also be found of definite interest to specialists in a wide range of fields (physicists, engineers, economists, linguists and others) that the science of probability touches on.