Multiple Mixing, Local Rank, and Joinings of Automorphisms of a Probability Space

We discuss selected unsolved problems on multiple mixing, structures of self-joinings, and the local rank of automorphisms of a probability space. For an account of the spectrum and entropy of the dynamical system that we use, see, for example, [I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic Theory, Springer, 1982].