  We apply elementary canonical methods for the quantization of 2+1 dimensional
gravity, where the dynamics is given by E. Witten's $ISO(2,1)$ Chern-Simons
action. As in a previous work, our approach does not involve choice of gauge or
clever manipulations of functional integrals. Instead, we just require the
Gauss law constraint for gravity to be first class and also to be everywhere
differentiable. When the spatial slice is a disc, the gravitational fields can
either be unconstrained or constrained at the boundary of the disc. The
unconstrained fields correspond to edge currents which carry a representation
of the $ISO(2,1)$ Kac-Moody algebra. Unitary representations for such an
algebra have been found using the method of induced representations. In the
case of constrained fields, we can classify all possible boundary conditions.
For several different boundary conditions, the field content of the theory
reduces precisely to that of 1+1 dimensional gravity theories. We extend the
above formalism to include sources. The sources take into account self-
interactions. This is done by punching holes in the disc, and erecting an
$ISO(2,1)$ Kac-Moody algebra on the boundary of each hole. If the hole is
originally sourceless, a source can be created via the action of a vertex
operator $V$. We give an explicit expression for $V$. We shall show that when
acting
