  We review two different methods of calculating Witten's invariant: a
stationary phase approximation and a surgery calculus. We give a detailed
description of the 1-loop approximation formula for Witten's invariant and of
the technics involved in deriving its exact value through a surgery
construction of a manifold. Finally we compare the formulas produced by both
methods for a 3-dimensional sphere S^3 and a lens space L(p,1).
