  We give a derivation of the Verlinde formula for the $G_{k}$ WZW model from
Chern-Simons theory, without taking recourse to CFT, by calculating explicitly
the partition function $Z_{\Sigma\times S^{1}}$ of $\Sigma\times S^{1}$ with an
arbitrary number of labelled punctures. By a suitable gauge choice,
$Z_{\Sigma\times S^{1}}$ is reduced to the partition function of an Abelian
topological field theory on $\Sigma$ (a deformation of non-Abelian BF and
Yang-Mills theory) whose evaluation is straightforward. This relates the
Verlinde formula to the Ray-Singer torsion of $\Sigma\times S^{1}$. We derive
the $G_{k}/G_{k}$ model from Chern-Simons theory, proving their equivalence,
and give an alternative derivation of the Verlinde formula by calculating the
$G_{k}/G_{k}$ path integral via a functional version of the Weyl integral
formula. From this point of view the Verlinde formula arises from the
corresponding Jacobian, the Weyl determinant. Also, a novel derivation of the
shift $k\ra k+h$ is given, based on the index of the twisted Dolbeault complex.
