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A review of the appearence of integrable structures in the matrix modeldescription of $2d$-gravity is presented. Most of ideas are demonstrated at thetechnically simple but ideologically important examples. Matrix models areconsidered as a sort of "effective" description of continuum $2d$ field theoryformulation. The main physical role in such description is played by theVirasoro-$W$ constraints which can be interpreted as a certain unitarity orfactorization constraints. Bith discrete and continuum (Generalized Kontsevich)models are formulated as the solutions to those discrete (continuous)Virasoro-$W$ constraints. Their integrability properties are proven usingmostly the determinant technique highly related to the representation in termsof free fields. The paper also contains some new observations connected toformulation of more general than GKM solutions and deeper understanding oftheir relation to $2d$ gravity.Comment: (based on lectures given at the Niels Bohr Institute) NORDITA-93/21,  FIAN/TD-05/93, 70 pp, late

INTEGRABLE STRUCTURES IN MATRIX MODELS AND PHYSICS OF 2D GRAVITY