Table of contents

Projective geometry

Lecture 1: Introduction
Lecture 2: Projective spaces
Lecture 3: General position and Pappus’ theorem
Lecture 4: Desargues’ theorem
Lecture 5: Projective transformations
Lecture 6: Cross-ratio
Lecture 7: Complete quadrilateral and quadrangular sets
Lecture 8: Projective involutions and Moebius tetrahedra
Lecture 9: Fundamental theorem of real projective geometry
Lecture 10: Duality
Lecture 11: Conics in Euclidean geometry
Lecture 12: Quadratic forms and conics in projective geometry
Lecture 13: Pencils of conics and Pascal’s theorem
Lecture 14: Polarity
Lecture 15: Polar triangle and Brianchon’s theorem
Lecture 16: Quadrics and orthogonal transformations

Hyperbolic geometry

Lecture 17: Hyperbolic space and hyperbolic lines
Lecture 18: Geodesics and projective model of hyperbolic space
Lecture 19: Klein model and hyperbolic lines
Lecture 20: Angles in Klein model
Lecture 21: Stereographic projection
Lecture 22: Poincare disc model
Lecture 23: Geodesics and Poincare half-space model
Lecture 24: Hyperbolic metric in half-plane model and hypperbolic triangles
Lecture 25: Hyperbolic Pythagoras’ theorem and hyperbolic isometries in the half-plane model

Moebius geometry

Lecture 26: Klein Erlangen program and Moebius geometry
Lecture 27: Sphere model and projective model of Moebius geometry
Lecture 27: Euclidean model of Moebius geometry and Moebius transformations as projective transformations

Last lecture: Nice pictures …