In this talk I'll explain what is a (marked) hyperbolic structure on a surface. Thurston proved that one can get from any hyperbolic structure to any other by performing an 'earthquake' along some geodesics. The first published account of this theorem was in an appendix to a paper by Steven Kerckhoff, which considered compact surfaces only. Later Thurston published a different proof which works for any hyperbolic surfaces, and I'll present this theorem.
No prior knowledge of hyperbolic geometry is necessary - I will introduce basic geometry of the hyperbolic plane. It would be helpful to have seen classification of surfaces before, and covering space theory.