Table of Contents
Introduction to Riemann Surfaces
The Riemann-Hurwitz Formula and Holomorphic Maps of Riemann Surfaces
Homotopy, The Fundamental Group, Covering Spaces and Hurwitz Numbers
Monodromy Representations, The Symmetric Group, and Hurwitz Numbers
The Cut-and-Join Equation
Hurwitz Theory in Positive Characteristic
Tropical Hurwitz Numbers
Hurwitz Spaces and the Moduli Space of Curves
Hurwitz Numbers and String Theory