Matrix models as conformal field theories

In these notes we explain how the asymptotic properties of correlation functions of U(N) invariant matrix integrals can be derived by means of conformal field theory. In the large N limit such CFT describe gaussian field on a Riemann surface. Our basic example is the hermitian matrix model. We give an explicit operator construction of the corresponding collective field theory in terms of a bosonic field on a hyperelliptic Riemann surface, with special operators associated with the branch points, The quasiclassical expressions for the spectral kernel and the joint eigenvalue probabilities are then easily obtained as correlation functions of current, fermionic and twist operators.