  In 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.
