  We present a semiclassical approach to n-point spectral correlation functions
of quantum systems whose classical dynamics is chaotic, for arbitrary n. The
basic ingredients are sets of periodic orbits that have nearly the same action
and therefore provide constructive interference. We calculate explicitly the
first correlation functions, to leading orders in their energy arguments, for
both unitary and orthogonal symmetry classes. The results agree with
corresponding predictions from random matrix theory, thereby giving solid
support to the conjecture of universality.
