Chapter 1. Differential Geometry 1.1 Manifolds 1.2 Tangent Vectors 1.3 Vector Fields, Integral Curves, and Flows 1.4 Tensors and Tensor Fields on Manifolds 1.5 The Action of Smooth Maps on Tensor Fields 1.6 Lie Derivatives 1.7 Derivative Operators and Geodesics 1.8 Curvature 1.9 Metrics 1.10 Hypersurfaces 1.11 Volume Elements Chapter 2. Classical Relativity Theory 2.1 Relativistic Spacetimes 2.2 Temporal Orientation and "Causal Connectibility" 2.3 Proper Time 2.4 Space/Time Decomposition at a Point and Particle Dynamics 2.5 The Energy-Momentum Field Tab 2.6 Electromagnetic Fields 2.7 Einstein's Equation 2.8 Fluid Flow 2.9 Killing Fields and Conserved Quantities 2.10 The Initial Value Formulation 2.11 Friedmann Spacetimes Chapter 3. Special Topics 3.1 Gödel Spacetime 3.2 Two Criteria of Orbital (Non-)Rotation 3.3 A No-Go Theorem about Orbital (Non-)Rotation Chapter 4. Newtonian Gravitation Theory 4.1 Classical Spacetimes 4.2 Geometrized Newtonian Theory—First Version 4.3 Interpreting the Curvature Conditions 4.4 A Solution to an Old Problem about Newtonian Cosmology 4.5 Geometrized Newtonian Theory—Second Version