Applications of the Riemann surfaces in physics: Moduli spaces

In this work, the physical applications of Riemann surfaces are taken into account, and the moduler spaces of Riemann surfaces in particular are considered. The first part of this work, which consists of four chapters, is devoted to the introduction of moduli spaces and string theory is briefly introduced. In the second part, some curves' moduli spaces are obtained. The third chapter is devoted to Riemann surfaces and the world-sheet. Specifically, three string effects and Schwarz-Cristoffel transformations have been studied. In the fourth and last section, moduli spaces of Riemann surfaces are obtained. This work is a compilation.