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Preface Chapter 1.Euclid Reading Euclid After Euclid The Discovery of Non-Euclidean Geometry Gaps in Euclid's Arguments Modem Axiom Systems Exercises Chapter 2.Incidence Geometry Axiomatic Systems The Axioms of Incidence Geometry Interpretations and Models of Incidence Geometry Some Nonmodels Consistency and Independence Some Infinite Models Parallel Postulates Theorems in Incidence Geometry Exercises Chapter 3.Axioms for Plane Geometry Points and Lines Distance Segments Rays Plane Separation Convex Sets Exercises Chapter 4.Angles Angles Betweenness of Rays The Interior of an Angle Exercises Chapter 5.Triangles Definitions Intersections of Lines and Triangles Congruent Triangles Inequalities More Congruence Theorems Exercises Chapter 6.Models of Neutral Geometry The Cartesian Model The Poincare Disk Model Some Nonmodels Independence of the Neutral Geometry Postulates Exercises Chapter 7.Perpendicular and Parallel Lines Perpendicular Lines Parallel Lines Exercises Chapter 8.Polygons Polygons