Reidemeister torsion, hyperbolic three-manifolds, and character varieties

This is a survey on Reidemeister torsion for hyperbolic three-manifolds of finite volume. Torsions are viewed as topological invariants and also as functions on the variety of representations in $\operatorname{ SL}_2(\mathbb C)$. In both cases, the torsions may also be computed after composing with finite dimensional representations of ${\mathrm{SL}}_2(\mathbb{C})$. In addition the paper deals with the torsion of the adjoint representation as a function on the variety of ${\mathrm{PSL}}_{n+1}(\mathbb{C})$-characters, using that the first cohomology group with coefficients twisted by the adjoint is the tangent space to the variety of characters.