2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54326The main part of this presentation is a review of the previous original works on the perturbative covariant approach to the $2$-dimensional quantum gravity. We discuss the renormalization of the two-dimensional dilaton gravity in a harmonic gauge, the form of the quantum corrections to the classical potential, and the conditions of Weyl invariance in a theory of string coupled to $2d$ quantum gravity.LaTeX, 16 pages, no figures, Talk given at the VI Seminar "Quantum Gravity" (Institute for Nuclear Research, Moscow, June, 1995)High Energy Physics - Theorytext