[en] 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_ΣxS¹ of ΣxS¹ with an arbitrary number of labelled punctures. By a suitable gauge choice, Z_ΣxS¹ is reduced to the partition function of an Abelian topological field theory on Σ (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 ΣxS¹. 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→k+h is given, based on the index of the twisted Dolbeault complex. (author). 28 refs