Kolmogorov's Heritage in Mathematics

From the reviews:

"Andrei N. Kolmogorov (1903-1987) was one of the most prolific and influential mathematicians of the twentieth century. … this collection would be read by those who hold only a bachelor’s degree in mathematics, computer science or physics, and more generally, by those interested in mathematical ideas. … This impressive collection gives the reader an understanding of the depth and breadth of Kolmogorov’s contributions to mathematics. Each chapter includes a substantial list of references that invite further reading." (Elena Anne Marchisotto, MathDL, December, 2007)

"The object of Kolmogorov’s Heritage in Mathematics is to enable the general mathematical reader (educated to master’s level) to grasp something of Kolmogorov’s achievements. … I can judge, it is successful in its aim. … those mathematicians with a sense of history, who wish to place themselves within the general culture of mathematics, will find this book a worthy memorial to a great man." (T. W. Korner, SIAM reviews, Vol. 50 (4), December, 2008)

Most mathematicians prove what they can, Kolmogorov belonged to a select group who proved what they want. In this book, several world experts present one part of the mathematical heritage of Kolmogorov. Each chapter treats one of his research themes or a subject invented as a consequence of his discoveries. The authors present his contributions, his methods, the perspectives he opened, and the way in which this research has evolved. Coverage also includes examples of recent applications and a presentation of the modern prospects. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details.