A rigorous development of metric and synthetic approaches to Euclidean and non-Euclidean geometries using an axiomatic format. Similarities and differences among definitions, axioms, theorems, and postulates of non-Euclidean geometries will be considered. The relationship of these geometries to Euclidean geometry will also be studied. Fall. Credit, 3 semester hours. PREREQ: MAT 2300; PREREQ or COREQ: MAT 3150.