## The Klein View of Geometry |

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We will describe several geometries in terms of groups and show how they are related.

**table of contents**

- introduction
- the klein view
- symmetries and symmetry groups
- the euclidean group
- the similarity group
- the inversive group
- the hyperbolic group
- the affine group
- the projective group
- fundamental theorems
- subgroups and their geometries
- geometrical invariants
- a weird geometry
- models of hyperbolic geometry
- hyperbolic and projective geometry
- a hyperbolic model of euclidean geometry
- concluding remarks