FCNSMAQFR4 credits This course takes a modern approach to geometry based on group theory and the Erlangen Programm making possible the survey of a wide spectrum of geometries, Euclidean and non-Euclidean. Geometries treated include neutral, Euclidean, spherical, and hyperbolic. The discovery of these geometries in the 19th century caused a scientific and philosophical revolution second only to the Copernican revolution.