  The article consists of a survey on analytic and topological torsion.
Analytic torsion is defined in terms of the spectrum of the analytic Laplace
operator on a Riemannian manifold, whereas topological torsion is defined in
terms of a triangulation. The celebrated theorem of Cheeger and M\"uller
identifies these two notions for closed Riemannian manifolds. We also deal with
manifolds with boundary and with isometric actions of finite groups. The basic
theme is to extract topological invariants from the spectrum of the analytic
Laplace operator on a Riemannian manifold.
