  This is an extended version of a series of talks I held at the University of
Bochum in 2017 about limit theorems for non-linear functionals of stationary
Gaussian random fields.
  The goal of these talks was to give a fairly detailed introduction to the
theory leading to such results, even if some of the results are presented
without proof. On the other hand, I gave a simpler proof for some of the
results. (The proofs omitted from this text can be found in my Springer Lecture
Note Multiple Wiener--Ito Integrals.
  In this note first I discuss the spectral representation of the covariance
function of a Gaussian stationary rendom field by means of the spectral measure
and the representation of the elements of the random field by means of a random
integral with respect to the random spectral measure. Then I construct the
multiple random integrals with respect to the random spectral measure and prove
their most important properties. Finally I show some interesting applications
of these multiple random integrals. In particular, I prove some non-trivial
non-Gaussian limit theorems
