The purpose of this course is to learn the historical development of Euclidean and non-Euclidean geometries and examine the similarities and differences between them.

The origin of Euclidean and non-Euclidean geometries, axiomatic method, primitive concepts of geometry, logical deficiencies in Euclidean geometry, Euclid’s parallel postulate and some substitutes for Euclid’s parallel postulate, neutral geometry, Bolyai-Lobachevskian geometry (hyperbolic geometry), Riemannian geometry (elliptic geometry), comparison for Euclidean and non-Euclidean plane geometries, projective geometry, affine plane and projective plane, the applications for hyperbolic plane.