50 years of Kolmogorov entropy: history and new prospects

In 1958 A. N. Kolmogorov published in DAN the paper about entropy as new metric invariant of the measure preserving transforamations. This article with other two which were published several years before, changed the face of the theory of dynamical systems and its role in mathematics. Nevertheles some ideas which are very closed to Kolmogorov's one were not sufficiently developed or even emphasized.
Entropy is only one of the seres of the invarinats which appear when we consider the dynamics of the metric spaces with measures. It is possible to define whole spectrum of such invariants. The investigation of the dynamics of the metric spaces is fruitful for other probelms of combinatorics and stochastic processes.
No special knowledges for understanding of the talk are needed.