## 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 …