Non-Euclidean geometry

This sixth edition explores non-Euclidean geometries in two and three dimensions, treating them as specializations of real projective geometry. It develops these concepts synthetically through axioms of points, lines, planes, incidence, order, and continuity, without initially focusing on distance or angle measurements. The book then introduces homogeneous coordinates and colineations, leading to elliptic isometries. It also details how elliptic and hyperbolic geometries are derived from real projective geometry by specializing polarities, making it suitable for readers with a background in algebra and group theory.