2-DIMENSIONAL QUANTUM-GRAVITY, MATRIX MODELS AND STRING THEORY

We review some results of the recent progress in understanding two-dim ensional quantum gravity and low-dimensional string theories based on the lattice approach. The possibility to solve the lattice models exac tly comes from their equivalence to large N matrix models. We describe various matrix models and their continuum limits, and discuss in some detail the phase structure of Hermitian one-matrix models. For the on e-dimensional matrix model we discuss its field theoretic formulation through a collective field method and summarize some perturbative resu lts. We compare the results obtained from matrix models to the results in the continuum approach to string theory.