After successful completion of the course, students are able to use the knowledge and to apply the methods specified in the curriculum:

They are familiar with abstractions of geometric notions and know various geometries and relations between them. Specifically they know the fundamentals and historical and scientific significance of the hyperbolic geometry.

Axiomatic method, Euclid's axiom of parallels and development of the hyperbolic non-euclidean geometry; models of hyperbolic non-euclidean geometry; other non-euclidean geometries (e.g., elliptic geometry, isotropic geometry, cyclography).

Lecture.

Oral exam.

Initially, lectures will follow John Stillwell, The four Pillars of Geometry; Springer (2005).  Please organize access to a copy by the start of the lectures.