 Foundations
 The linear groups
 Examples of linear groups
 Isometries of R^{n}
 Isometries of the line
 Isometries of the plane
 Isometries in 3 dimensions
 Symmetry groups in the plane
 Frieze groups
 Platonic solids
 Finite rotation groups of R^{3}
 Full finite symmetry groups in R^{3}
 Affine geometry

 Affine theorems
 Similarity geometry
 Projective spaces
 Homogeneous coordinates
 The projective groups
 More projective groups
 Some theorems in plane projective geometry
 Introduction to topology
 Surfaces
 The Connected Sum
 Planar models
 The Euler Characteristic
 The Classification Theorem

Summary of results
Geometry quotations
More geometry quotations

Exercises

 Exercises 1
 Exercises 2
 Exercises 3
 Exercises 4
 Exercises 5

 Exercises 6
 Exercises 7
 Exercises 8
 Exercises 9
