0. Overture I Geometry and mechanics in at spacetime 1. Special relativity 2. Vectors in at spacetime 3. Coordinates 4. Linear slot machines 5. The metric II Curvature and general relativity 6. Finding a theory of gravitation 7.

Parallel lines and the covariant derivative 8. Free fall and geodesics 9. Geodesic equations and connection coecients 10. Making measurements in relativity 11. Riemann curvature and the Ricci tensor 12. The energy-momentum tensor 13. The gravitational field equations 14. The triumphs of general relativity III Cosmology 15.

An introduction to cosmology 16. Robertson-Walker spaces 17. The Friedmann equations 18. Universes of the past and future 19. Causality, infinity and horizons IV Orbits, stars and black holes 20. Newtonian orbits 21. The Schwarzschild geometry 22. Motion in the Schwarzschild geometry 23.

Orbits in the Schwarzschild geometry 24. Photons in the Schwarzschild geometry 25. Black holes 26. Black-hole singularities 27. Kruskal-Szekeres coordinates 28. Hawking radiation 29. Charged and rotating black holes V Geometry 30. Classical curvature 31.

A reintroduction to geometry 32. Differential forms 33. Exterior and Lie derivatives 34. Geometry of the connection 35. Riemann curvature revisited 36. Cartan's method 37. Duality and the volume form 38. Forms, chains and Stokes' theorem VI Classical and quantum fields 39.

Fluids as dry water 40. Lagrangian field theory 41. Inflation 42. The electromagnetic field 43. Charge conservation and the Bianchi identity 44. Gauge fields 45. Weak gravitational fields 46. Gravitational waves 47.

The properties of gravitons 48. Higher-dimensional spacetime 49. From classical to quantum gravity 50. The Big-Bang singularity A. Further reading B. Conventions and notation C. Manifolds and bundles D. Embedding E.

Answers to selected problems.