0 Preliminaries.- 0.0 Review and notation.- 0.1 Physics background.- 0.2 Preview of relativity.- 1 Spacetimes.- 1.0 Review and notation.- 1.1 Causal character.- 1.2 Time orientability.- 1.3 Spacetimes.- 1.4 Examples of spacetimes.- 2 Observers.- 2.0 Mathematical preliminaries.- 2.1 Observers and instantaneous observers.- 2.2 Gyroscope axes.- 2.3 Reference frames.- 3 Electromagnetism and matter.- One: Basic Concepts.- Two: Interactions.- Three: Other Matter Models.- 4 The Einstein field equation.- 4.0 Review and notation.- 4.1 The Einstein field equation.- 4.2 Ricci flat spacetimes.- 4.3 Gravitational attraction and the phenomenon of collapse.- 5 Photons.- 5.0 Mathematical preliminaries.- 5.1 Photons.- 5.2 Light signals.- 5.3 Synchronizable reference frames.- 5.4 Frequency ratio.- 5.5 Photon distribution functions.- 5.6 Integration on lightcones.- 5.7 A photon gas.- 6 Cosmology.- 6.0 Review, notation and mathematical preliminaries.- 6.1 Data.- 6.2 Cosmological models.- 6.3 The Einstein-de Sitter model.- 6.4 Simple cosmological models.- 6.5 The early universe.- 6.6 Other models.- 6.7 Appendix: Luminosity distance in the Einstein-de Sitter model.- 7 Further applications.- 7.0 Review and notation.- 7.1 Preview.- 7.2 Stationary spacetimes.- 7.3 The geometry of Schwarzschild spacetimes.- 7.4 The solar system.- 7.5 Black holes.- 7.6 Gravitational plane waves.- 8 Optional exercises: relativity.- 8.1 Lorentzian algebra.- 8.2 Differential topology and geometry.- 8.3 Chronology and causality.- 8.4 Isometries and characterizations of gravitational fields.- 8.5 The Einstein field equation.- 8.6 Gases.- 9 Optional exercises: Newtonian analogues.- 9.0 Review and notation.- 9.1 Maxwell's equations.- 9.2 Particles.- 9.3 Gravity.- Glossary of symbols.- Index of basic notations.