The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of
strongly dependent random variables that play an important role in probability theory or in
statistical physics. Here non-linear functionals of stationary Gaussian fields are considered
and it is shown that the theory of Wiener-Itô integrals provides a valuable tool in their
study. More precisely a version of these random integrals is introduced that enables us to
combine the technique of random integrals and Fourier analysis. The most important results of
this theory are presented together with some non-trivial limit theorems proved with their help.
This work is a new revised version of a previous volume written with the goal of giving a
better explanation of some of the details and the motivation behind the proofs. It does not
contain essentially new results it was written to give a better insight to the old ones. In
particular a more detailed explanation of generalized fields is included to show that what is
at the first sight a rather formal object is actually a useful tool for carrying out heuristic
arguments.
