Appears in collection : 2023 - T1A - WS1 - Quantum gravity and random geometry

I will explain the idea of topological recursion, its implementation for the enumeration of maps (and of large maps), and mention other applications to compute integrals over the moduli space of Riemann surfaces $M_{g,n}$. I will introduce the idea of geometric recursion which in certain cases allows for a fully geometric proof that topological recursion solves such problems.