This famous little book was first published in German in 1933 and in Russian a few years later, setting forth the axiomatic foundations of modern probability theory and cementing the author's reputation as a leading authority in the field. It remains a foundational text for the understanding of probability theory, important both to students beginning a serious study of the topic and to historians of modern mathematics. AUTHOR: A. N. (Andrei Nikolaevich) Kolmogorov (1903-87) was a prominent Russian mathematician who made significant contributions to many areas of math, including probability theory, topology, logic, turbulence, and mechanics. His other Dover books are Introductory Real Analysis, Elements of the Theory of Functions and Functional Analysis (with S.V. Fomin), and Mathematics, Its Content, Methods and Meaning (with A. D. Aleksandrov and M. A. Lavrent'ev). In his many years on the faculty of Moscow State University, Dr. Kolmogorv's doctoral students included several who became prominent 20th-century mathematicians.