# Vortrag

Planar maps are graphs drawn on the sphere in such a way that their edges do not intersect, seen up to deformations of the underlying sphere. Given a map $m$, we can equip the set of its vertices with the graph distance $d$, where $d(x,y)$ is the smallest number of edges of any path between $x$ and $y$. Doing so makes $m$ into a metric space; picking $m$ at random is a first step towards defining a "natural" random metric space: the Brownian map. I will present some objects and ideas of random maps.