# Hurwitz numbers of Riemann sphere and integrable hierarchies.

The Hurwitz numbers count the topologically non-equivalent types

of finite ramified coverings of a given Riemann surface. When the base

Riemann surface is the Riemann sphere, these numbers are known to be

related to intersection numbers of the Hodge classes and the psi classes

on the moduli space of stable complex curves. On the other hand, the

same numbers can be expressed in a genuinely combinatorial form in terms

of symmetric groups. The latter expression reveals that the generating

functions of a particular class of Hurwitz numbers of the Riemann sphere

become tau functions of the KP hierarchy and its relatives. I will review

these facts for non-experts of integrable systems.