DEGENERATIONS OF HYPERBOLIC STRUCTURES ON SURFACES

These are lecture notes from the summer school on Geometry, Topology and Dynamics of Character Varieties at the Institute for Mathematical Sciences, National University of Singapore in July of 2010. The objective is to give an introduction to some of the tools used in studying the degeneration of hyperbolic structures on surfaces as developed by Thurston, and in particular to describe his construction of a compactification of Teichmüller space.