A hyperbolic manifold is a manifold with constant negative curvature. Riemann uniformisation and Thurston-Perelman geometrisation show the existence in dimension 2 and 3 of a big variety of hyperbolic manifolds, but their role in four and higher dimension is not yet clear.
In this seminar we introduce the basic theory of hyperbolic manifolds and construct various examples using regular polytopes in dimensions 2, 3, and 4.