  The aim of the present survey paper is to provide an accessible introduction
to a new chapter of representation theory - harmonic analysis for
noncommutative groups with infinite-dimensional dual space.
  I omitted detailed proofs but tried to explain the main ideas of the theory
and its connections with other fields. The fact that irreducible
representations of the groups in question depend on infinitely many parameters
leads to a number of new effects which never occurred in conventional
noncommutative harmonic analysis. A link with stochastic point processes is
especially emphasized.
  The exposition focuses on a single group, the infinite symmetric group. The
reason is that presently this particular example is worked out the most.
Furthermore, the infinite symmetric group can serve as a very good model for
more complicated groups like the infinite-dimensional unitary group.
