Abstract: The intention of this talk is to present a brief introduction to torsion invariants. These are invariants associated to smooth manifolds which generalize the Alexander polynomial and are closely related to Seiberg-Witten invariants in dimension three.

In the first part of the talk we will explain the definition of Reidemeister torsion - a combinatorial approach to torsion. We will also discuss how Turaev used his Euler structures to avoid certain ambiguities in the definition.

In the second part we will give a brief description of Ray-Singer torsion - an analytic approach to torsion. We will then introduce a new concept called co-Euler structures. These are in some sense dual to Euler structures and can be used to remove ambiguities in the definition of the Ray-Singer torsion.

From this perspective we will then describe the Cheeger-Müller (Bismut-Zhang) theorem, which tells that these two invariants basically coincide.