Complete Lorentzian 3-manifolds

Based on four lectures the authors gave in Almora on flat Lorentzian manifolds, these notes are an introduction to Lorentzian three-manifolds. In particular, we provide examples of quotients of Minkowski space by the actions of groups acting freely and properly discontinuously. Most of these notes deal with complete Lorentz manifolds whose fundamental groups are both free and non-abelian. We shall also look at Lorentz manifolds whose fundamental groups are solvable in some detail.