  Witten- Helffer-Sj\"ostrand theory is a considerable addition to the De Rham-
Hodge theory for Riemannian manifolds and can serve as a general tool to prove
results about comparison of numerical invariants associated to compact
manifolds analytically, i.e. by using a Riemannian metric, or combinatorially,
i.e by using a triangulation. In this presentation a triangulation, or a
partition of a smooth manifold in cells, will be viewed in a more analytic
spirit, being provided by the stable manifolds of the gradient of a nice Morse
function. WHS theory was recently used both for providing new proofs for known
but difficult results in topology, as well as new results and a positive
solution for an important conjecture about $L_2-$torsion, cf [BFKM]. This
presentation is a short version of a one quarter course I have given during the
spring of 1997 at OSU.
