Students are familiar with abstractions of geometric notions or objects and know about various geometries and their interrelations. In particular, they are familiar with the foundations and with the historical and scientific relevance of the hyperbolic non-euclidean geometry, and they know the basics of a systematic analysis of curves and surfaces by means of differential geometric methods.

Axiomatics of absolute geometry in the plane, free mobility; the hyperbolic plane and its models; other non-euclidean geometries, e.g., elliptic geometry.

The first part of the lectures will follow closely

J Stillwell: The four pillars of geometry; UTM Springer, New York (2005)