This is the second volume in a two-volume set,which provides a complete self-contained proof of the classification of geometries associated with sporadic simple groups: Petersen and tilde geometries. This volume contains a study of the representations of the geometries under consideration in GF(2)-vector spaces as well as in some non-abelian groups.

The central part is the classification of the amalgam of maximal parabolics,associated with a flag transitive action on a Petersen or tilde geometry.The classification is based on the method of group amalgams,the most promising tool in modern finite group theory.Through systematic of group amalgams,the authors establish a deep and important mathematical result.

Part 1 Representations
- General Features
- Terminology and notation
- Collinearity Graph
- Geometric hyperplanes
- Odd order subgroups
etc.

Part 2 Amalgams
- Method of group amalgams
- General strategy
- Some cohomologies
- Goldschmidt's theorem
- Factor amalgams
etc.