  Random matrices are used in fields as different as the study of
multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of
them are based on the study of a matrix integral. However, this term can be
confusing since the definition of a matrix integral in these two applications
is not the same. These two definitions, perturbative and non-perturbative, are
discussed in this chapter as well as their relation. The so-called loop
equations satisfied by integrals over random matrices coupled in chain is
discussed as well as their recursive solution in the perturbative case when the
matrices are Hermitean.
