In these lectures, the notion of the topological recursion is introduced through enumerative geometry problems, such as counting simple Hurwitz numbers and the number of lattice points on the moduli space of pointed curves.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/AT2015