  The last theme of Kolmogorov's mathematics research was algorithmic theory of
information, now often called Kolmogorov complexity theory. There are only two
main publications of Kolmogorov (1965 and 1968-1969) on this topic. So
Kolmogorov's ideas that did not appear as proven (and published) theorems can
be reconstructed only partially based on work of his students and
collaborators, short abstracts of his talks and the recollections of people who
were present at these talks.
  In this survey we try to reconstruct the development of Kolmogorov's ideas
related to algorithmic statistics (resource-bounded complexity, structure
function and stochastic objects).
