  These are the lectures notes of the course given at the Eleventh Modave
Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior
researchers in theoretical physics. We review in details the result of
Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$-
dimensional gravity with negative cosmological constant is described at the
classical level by Liouville theory. Boundary conditions implement the
asymptotic reduction in two steps: the first set reduces the $SL(2,\mathbb
R)\times SL(2,\mathbb R)$ Chern-Simons action, equivalent to the Einstein
action, to a non-chiral $SL(2,\mathbb R)$ Wess-Zumino-Witten model, while the
second set imposes constraints on the WZW currents that reduce further the
action to Liouville theory. We discuss the issues of considering the latter as
an effective description of the dual conformal field theory describing AdS$_3$
gravity beyond the semi-classical regime.
