  This paper is based on the author's talk at the 2012 Workshop on Geometric
Methods in Physics held in Bialowieza, Poland. The aim of the talk is to
introduce the audience to the Eynard-Orantin topological recursion. The
formalism is originated in random matrix theory. It has been predicted, and in
some cases it has been proven, that the theory provides an effective mechanism
to calculate certain quantum invariants and a solution to enumerative geometry
problems, such as open Gromov-Witten invariants of toric Calabi-Yau threefolds,
single and double Hurwitz numbers, the number of lattice points on the moduli
space of smooth algebraic curves, and quantum knot invariants. In this paper we
use the Laplace transform of generalized Catalan numbers of an arbitrary genus
as an example, and present the Eynard-Orantin recursion. We examine various
aspects of the theory, such as its relations to mirror symmetry, Gromov-Witten
invariants, integrable hierarchies such as the KP equations, and the
Schroedinger equations.
