  The Ray-Singer torsion for a compact smooth hyperbolic 3-dimensional manifold
${\cal H}^3$ is expressed in terms of Selberg zeta-functions, making use of the
associated Selberg trace formulae. Applications to the evaluation of the
semiclassical asymptotics of the Witten's invariant for the Chern-Simons theory
with gauge group SU(2) as well as to the sum over topologies in 3-dimensional
quantum gravity are presented.
