
We start (with chapters 1, 2, 4, and 5) by examining the notion of straightness (to define lines in our surfaces) and the properties of lines on the various surfaces. The second part of the course (chapters 3, 6, and 9.12) examines transformations, congruence, angles and triangles. Next, we investigate maps of the sphere and hyperbolic plane (chapters 15 and 16). The final part of the course (chapters 7, 8, 9.34, and 10) deals with the parallel postulate and related notions.