  This text is written based on the author's publications during the period
from 1991 to 2001. The work is devoted to the theory of Markov intertwining
operators and joinings of measure-preserving group actions, as well as to their
applications to study asymptotic properties of dynamical systems. Special
attention is paid to Rokhlin's problems on multiple mixing and multiple
spectrum. The development of these topics over the past twenty years has not
been discussed. In fact many results on joinings have frozen in time, many
questions have remained open without losing their relevance, but probably have
ceased to excite interest due to difficulties. For example, it is not known
whether the minimal self-joinings of order 2 imply all orders? Is there a
non-trivial pairwise independent joining for a weakly mixing system of zero
entropy? What can be said about such joinings for transformations with small
local rank? These questions are ripe for a long time, and the author reminds
the reader about them, combining his story with numerous partial and related
results.
