This book by A.N.

Kolmogorov is a foundational text for understanding probability theory, cementing the author's reputation as a leading authority in the field.

It remains important both to students beginning a serious study of probability and to historians of modern mathematics.

The treatment begins with an introduction to elementary theory of probability and infinite probability fields, followed by chapters on random variables, mathematical expectations, and conditional probabilities and mathematical expectations.

The book concludes with a chapter on the law of large numbers, an Appendix on zero-or-one in the theory of probability, and detailed bibliographies.

With its historical significance and practical applications, this book is suitable as a text for advanced undergraduates and graduate students in mathematics.