I. Bierberbach's Three Theorems. - 1. Rigid Motions. - 2. Examples. - 3. Bierberbach's First Theorem. - 4. Bierberbach's Second Theorem. - 5. Digression Group Extensions. - 6. Digression Integral Repesentations of Finite Groups. - 7. Bieberbach's Third Theorem and Some Remarks. - II. Flat Riemannian Manifolds. - 1. Introduction. - 2. A Tiny Bit of Differential Topology. - 3. Connections and Curvature. - 4. Riemannian Structures. - 5. Flat Manifolds. - 6. Conjectures and Counterexamples. - III. Classification Theorems. - 1. The Algebraic Structure of Bieberbach Groups. - 2. A General Classification Scheme for Bieberbach Groups. - 3. Digression Cohomology of Groups. - 4. Examples. - 5. Holonomy Groups. - IV. Holonomy Groups of Prime Order. - 1. Introduction. - 2. Digression Some Algebraic Number Theory. - 3. Modules over the Cyclotomic Ring. - 4. Modules over Groups of Prime Order. - 5. The Cohomology of Modules over Groups of Prime Order. - 6. The Classification Theorem. - 7. ?p-manifolds. - 8. An Interesting Example. - 9. The Riemannian Structure of Some ?p manifolds. - V. Automorphisms. - 1. The Basic Diagram. - 2. The Hochschild-Serre Exact Sequence. - 3. 9-Diagrams. - 4. Automorphisms of Group Extensions. - 5. Automorphisms of Bieberbach Groups. - 6. Automorphisms of Flat Manifolds. - 7. Automorphisms of ?p-manifolds. Language: English