  We explain how Gaussian integrals over ensemble of complex matrices with
source matrices generate Hurwitz numbers of the most general type, namely,
Hurwitz numbers with arbitrary orientable or non-orientable base surface and
arbitrary profiles at branch points. We use the Feynman diagram approach. The
connections with topological theories and also with certain classical and
quantum integrable theories in particular with Witten's description of
two-dimensional gauge theory are shown.
