  This preprint is the introduction of my habilitation thesis for Paris7
university. It is a sumary of a collection of works on the 2 matrix model. In
an introduction, 3 different and unequivalent definitions of matrix models are
given (convergent model, model with fixed filling fractions on contours, and
formal model). Then, a sumary of properties of differential systems satisfied
by biorthogonal polynomials, in particular spectral duality and Riemann-Hilbert
problem. Then, a section on loop equations and algebraic geometry formulation
of the large N expansion. Then, a conjecture for the asymptotics of
biorthogonal polynomials.
