François David: Random matrices and two dimensional quantum gravity
This course is a short introduction to random matrices and applications to twodimensional quantum gravity. I shall review discrete formulations of two dimensional quantum gravity, planar maps, and the relations with the large N limit of random matrices (planar limit), and various methods to solve random matrix models: Coulomb gas methods, recursion (loop) equations, orthogonal polynomials, etc. The topological expansion, the double scaling limit and KPZ relations will be reviewed. Finally, the links between matrix models, topological 2D gravity and strings (the study of moduli space of surfaces) will be briefly discussed.
Main references that I shall use (the not too advanced material) is:

Lectures notes by Bertrand Eynard about random matrices and surfaces
Random matrices: http://ipht.cea.fr/Docspht/articles/t01/014/public/publi.pdf
Random matrices: arXiv:1510.04430

A book by B. Eynard (CRM Aisenstadt Chair lectures in Montreal of 2015)
Counting Surfaces: http://www.springer.com/us/book/9783764387969
Additional references about the relation between matrix models, Liouville theory, CFT and 2D gravity (but I shall only deal with some very introductory and basic elements) are:

The review by Y. Nakayama
Liouville Field Theory  A decade after the revolution: arXiv:hepth/0402009

Les Houches lectures by B. Duplantier
Conformal Random Geometry: arXiv:mathph/0608053