  We analyze 2+1-dimensional gravity in the framework of quantum gauge theory.
We find that Einstein gravity has a trivial physical subspace which reflects
the fact that the classical solution in empty space is flat. Therefore we study
massive gravity which is not trivial. In the limit of vanishing graviton mass
we obtain a non-trivial massless theory different from Einstein gravity. We
derive the interaction from descent equations and obtain the cosmological
topologically massive gravity. However, in addition to Einstein and
Chern-Simons coupling we need coupling to fermionic ghost and anti-ghost fields
and to a vector-graviton field with the same mass as the graviton.
