2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54739In this paper, based on the author's lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan--Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at $n$ marked points are given. The covariant derivatives are expressed in terms of ``dynamical $r$-matrices'', a notion borrowed from integrable systems. The case of marked points moving on a fixed Riemann surface is studied more closely. We prove a universal form of the (projective) flatness of the connection: the covariant derivatives commute as differential operators with coefficients in the universal enveloping algebra -- not just when acting on conformal blocks.29 pages, LaTeX, to appear in the Proceedings of the 1995 les Houches Summer SchoolHigh Energy Physics - Theorytext