A nonperturbative approach to two dimensional quantum gravity is discussed using a double scaling limit of the matrix model. The operator formalism of the orthogonal polynomials gives an exact differential equation for the partition function of the 2 dimensional gravity as a function of string coupling constant. The different properties from existing perturbative theory are discussed. The correlation functions are constructed to all orders in the genus expansion. The extension of the matrix model to higher dimensioons is briefly discussed.