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During the last 15 years or so, and since the pioneering work of E. Wigner, F. Dyson and M.L. Mehta, random matrix theory, combinatorial and perco- lation questions have merged into a very lively area of research, pro ducing an outburst of ideas, techniques and connections; in particular, this area contains a number of strikingly beautiful gems. The purpose of these five Montreal lectures is to present some of these gems in an elementary way, to develop some of the basic tools and to show the interplay between these topics. These lec- tures were written to be elementary, informal and reasonably self-contained and are aimed at researchers wishing to learn this vast and beautiful subject. My purpose was to explain these topics at an early stage, rather than give the most general formulation. Throughout, my attitude has been to give what is strictly necessary to understand the subject. I have tried to provide the reader with plenty of references, although I may and probably will have omitted some of them; if so, my apologies!

Random and Integrable Models in Mathematics and Physics