This text for advanced undergraduates emphasizes the logical connections of the subject. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite.

Inhalt
1 Axioms for Plane Geometry.- 2 Some Neutral Theorems of Plane Geometry.- 3 Qualitative Description of the Hyperbolic Plane.- 4 ?3 and Euclidean Approximations in ?2.- 5 Differential Geometry of Surfaces.- 6 Quantitative Considerations.- 7 Consistency and Categoricalness of the Hyperbolic Axioms; The Classical Models.- 8 Matrix Representation of the Isometry Group.- 9 Differential and Hyperbolic Geometry in More Dimensions.- 10 Connections with the Lorentz Group of Special Relativity.- 11 Constructions by Straightedge and Compass in the Hyperbolic Plane.