The above picture shows examples of K-surfaces, i.e. surfaces with constant Gaussian curvature $K=-1$. The picture was made by Nicholas Schmitt and is part of the GeometrieWerkstatt Gallery. Instead of writing at length about the theory of K-surfaces and their relation to hyperbolic Geometry and the discrete Pendulum equation (as discussed in the class) , I will refer here to lecture notes of a course I gave at Beiing University in 2009.