The Constraint Equations.- The Penrose Inequality.- The Global Existence Problem in General Relativity.- Smoothness at Null Infinity and the Structure of Initial Data.- Status Quo and Open Problems in the Numerical Construction of Spacetimes.- The Einstein-Vlasov System.- Future Complete U(1) Symmetric Einsteinian Spacetimes, the Unpolarized Case.- Future Complete Vacuum Spacetimes.- The Cauchy Problem on Spacetimes That Are Not Globally Hyperbolic.- Cheeger-Gromov Theory and Applications to General Relativity.- Null Geometry and the Einstein Equations.- Group Actions on Lorentz Spaces, Mathematical Aspects:A Survey.- Gauge, Diffeomorphisms, Initial-Value Formulation, Etc..