An overview of the intersection theory on moduli spaces of curves

The purpose of the thesis is to introduce the notion of moduli space of curves and to present how we can develop an intersection theory on it. After an introductory chapter dedicated to the notion of moduli space, with a particular attention to the case of moduli spaces of smooth curves and of stable curves, we’ll develop in the next chapters the main ideas of the modern approach to the intersection theory. The definition of Chow ring and of the intersection product will be followed by some examples in order to show how these notions can be applied; finally, in the last part of the thesis we'll concentrate on the particular case of intersection theory on moduli spaces of genus 2 stable curves.