Matrix model tools and geometry of moduli spaces

The relation between matrix models and geometrical structures on moduli spaces of algebraic curves is reviewed. The description of discretized moduli spaces and the generating function for intersection indices (cohomological classes) on these spaces is presented by the matrix model with the logarithmic potential when using the stratification procedure to express integrals over open strata via integrals over compactified spaces. We review the constraint equations and related Virasoro algebras appearing in various matrix models paying the special attention to the interrelations between these models. The explicit solutions to matrix models in 1/N expansion are presented.