  We present a semiclassical explanation of the so-called
Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral
fluctuations in chaotic dynamics. We work with a generating function whose
semiclassical limit is determined by quadruplets of sets of periodic orbits.
The asymptotic expansions of both the non-oscillatory and the oscillatory part
of the universal spectral correlator are obtained. Borel summation of the
series reproduces the exact correlator of random-matrix theory.
