0: OvertureI Geometry and mechanics in at spacetime1: Special relativity2: Vectors in at spacetime3: Coordinates4: Linear slot machines5: The metricII Curvature and general relativity6: Finding a theory of gravitation7: Parallel lines and the covariant derivative8: Free fall and geodesics9: Geodesic equations and connection coecients10: Making measurements in relativity11: Riemann curvature and the Ricci tensor12: The energy-momentum tensor13: The gravitational field equations14: The triumphs of general relativityIII Cosmology15: An introduction to cosmology16: Robertson-Walker spaces17: The Friedmann equations18: Universes of the past and future19: Causality, infinity and horizonsIV Orbits, stars and black holes20: Newtonian orbits21: The Schwarzschild geometry22: Motion in the Schwarzschild geometry23: Orbits in the Schwarzschild geometry24: Photons in the Schwarzschild geometry25: Black holes26: Black-hole singularities27: Kruskal-Szekeres coordinates28: Hawking radiation29: Charged and rotating black holesV Geometry30: Classical curvature31: A reintroduction to geometry32: Differential forms33: Exterior and Lie derivatives34: Geometry of the connection35: Riemann curvature revisited36: Cartan's method37: Duality and the volume form38: Forms, chains and Stokes' theoremVI Classical and quantum fields39: Fluids as dry water40: Lagrangian field theory41: Inflation42: The electromagnetic field43: Charge conservation and the Bianchi identity44: Gauge fields45: Weak gravitational fields46: Gravitational waves47: The properties of gravitons48: Higher-dimensional spacetime49: From classical to quantum gravity50: The Big-Bang singularityA: Further readingB: Conventions and notationC: Manifolds and bundlesD: EmbeddingE: Answers to selected problems.