Formulae for calculating Hurwitz numbers

Abstract

In this paper, we aim to provide an accessible survey to various formulae for calculating single Hurwitz numbers. Single Hurwitz numbers count certain classes of meromorphic functions on complex algebraic curves and have a rich geometric structure behind them which has attracted many mathematicians and physicists. Formulation of the enumeration problem is purely of topological nature, but with connections to several modern areas of mathematics and physics.