The knowledge of Euclidean Geometry acquired in high school is used as a basis for generalization. Familiar Euclidean concepts and theorems are modified and extended to produce other geometries with unusual and interesting properties. Structure and formal proof are stressed. The non-Euclidean geometries' component for the course provides an opportunity to see that a modern theoretical model of the universe which depends on a complex non-Euclidean geometry supports Einstein's general theory of relativity.
