D-dimensional induced gauge theory as a solvable matrix model

We discuss basic features and new developments in recently proposed induced gauge theory solvable in any number of dimensions in the limit of infinite number of colours. Its geometrical (string) picture is clarified, using planar graph expansion of the corresponding matrix model. New analytical approach is proposed for this theory which is based on its equivalence to an effective two-matrix model. It is shown on some particular examples how the approach works. This approach may be applicable to a wide class of matrix models with tree-like quadratic couplings of matrices. (This talk was presented on the International Symposium on Lattice Field Theory "LATTICE-92" in Amsterdam, the Netherlands, 15-19 September 1992)