Representations of fundamental groups and 3-manifold topology

In 3-dimensional topology the great progress during the last two decades revealed that various properties of 3-manifolds are well understood from their fundamental groups. I will give an introduction to the study of splittings of 3-manifolds along surfaces, with an emphasis on an application of group representations. A fundamental and difficult problem in general is to find surfaces essentially embedded in a given 3-manifold. I will explain how such surfaces are detected by deformations of representations of the fundamental group, and what information of detected surfaces is described in terms of topological invariants derived from representations.