  A quantization of (2+1)-dimensional gravity with negative cosmological
constant is presented and quantum aspects of the (2+1)-dimensional black holes
are studied thereby. The quantization consists of two procedures. One is
related with quantization of the asymptotic Virasoro symmetry. A notion of the
Virasoro deformation of 3-geometry is introduced. For a given black hole, the
deformation of the exterior of the outer horizon is identified with a product
of appropriate coadjoint orbits of the Virasoro groups $\hat{diff S^1}_{\pm}$.
Its quantization provides unitary irreducible representations of the Virasoro
algebra, in which state of the black hole becomes primary. To make the
quantization complete, holonomies, the global degrees of freedom, are taken
into account. By an identification of these topological operators with zero
modes of the Liouville field, the aforementioned unitary representations
reveal, as far as $c \gg 1$, as the Hilbert space of this two-dimensional
conformal field theory. This conformal field theory, living on the cylinder at
infinity of the black hole and having continuous spectrums, can recognize the
outer horizon only as a it one-dimensional object in $SL_2({\bf R})$ and
realize it as insertions of the corresponding vertex operator. Therefore it can
not be a conformal field theory on the horizon. Two possible descriptions of
the horizon conformal field theory are proposed.
