  $G/G$ topological field theories based on $G_k$ WZW models are constructed
and studied. These coset models are formulated as Complex BRST cohomology in
$G^c_k$, the complexified level $k$ current algebra. The finite physical
spectrum corresponds to the conformal blocks of $G_k$ .The amplitudes for $G/G$
theories are argued to be given in terms of the $G_k$ fusion rules. The
$G_k/G_k$ character is the Kac-Weyl numerator of $G_k$ and is interpreted as an
index. The Complex BRST cohomology is found to contain states of arbitrary
ghost number. Intriguing similarities of $G/G$ to $c\leq 1$ matter systems
coupled to two dimensional gravity are pointed out.
