Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of the results from the class notes. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors). These notes are based on the first part of Wald's General Relativity and excludes the content of Part II (Advanced Topics) of the book.

1. Chapter 1. Introduction.
2. Chapter 2. Manifolds and Tensor Fields.
3. Chapter 3. Curvature.
4. Chapter 4. Einstein's Equation.
5. Chapter 5. Homogeneous, Isotropic Cosmology.
6. Chapter 6. The Schwarzschild Solution.
7. Appendix A. Topological Spaces.
8. Appendix B. Differential Forms, Integration, and Frobenius's Theorem.
9. Appendix C. Maps of Manifolds, Lie Derivatives, and Killing Fields.

Chapter 1. Introduction.

• Section 1.1. Introduction. Section 1.1 notes
• Section 1.2. Space and Time in Prerelativity Physics and in Special Relativity. Section 1.2 notes
• Section 1.3. The Spacetime Metric. Section 1.3 notes
• Section 1.4. General Relativity. Section 1.4 notes
• Study Guide 1

Chapter 2. Manifolds and Tensor Fields.

• Section 2.1. Manifolds. Section 2.1 notes
• Section 2.2. Vectors. Section 2.2 notes
• Supplement. Proofs of Theorems in Section 2.2. Beamer file of Section 2.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section 2.2. Print file of Section 2.2 proofs
• Section 2.3. Tensors; the Metric Tensor.
• Section 2.4. The Abstract Index Notation.
• Study Guide 2.

Chapter 3. Curvature.

• Section 3.1. Derivative Operators and Parallel Transport.
• Section 3.2. Curvature.
• Section 3.3. Geodesics.
• Section 3.4. Methods for Computing Curvature.
• Study Guide 3.

Chapter 4. Einstein's Equation.

• Section 4.1. The Geometry of Space in Prerelativity Physics; General and Special Covariance.
• Section 4.2. Special Relativity.
• Section 4.3. General Relativity.
• Section 4.4. Linearized Gravity: The Newtonian Limit and Gravitiation Radiation.
• Study Guide 4.

Chapter 5. Homogeneous, Isotropic Cosmology.

• Section 5.1. Homogeneity and Isotropy.
• Section 5.2. Dynamics of a Homogeneous, Isotropic Universe.
• Section 5.3. The Cosmological Redshift; Horizons.
• Section 5.4. The Evolution of Our Universe.
• Study Guide 5.

Chapter 6. The Schwarzschild Solution.

• Section 6.1. Derivation of the Schwarzschild Solution.
• Section 6.2. Interior Solutions.
• Section 6.3. Geodesics of Schwarzschild: Gravitational Redshift, Periholion Precession, Bending of Light, and Time Delay.
• Section 6.4. The Kruskal Extension.
• Study Guide 6.

Appendices.

• Appendix A. Topological Spaces.
• Appendix B. Differential Forms, Integration, and Frobenius's Theorem.
• Appendix C. Maps of Manifolds, Lie Derivatives, and Killing Fields.
• Study Guide A.

Additional Chapters from Part II, Advanced Topics.

• Chapter 7. Methods for Solving Einstein's Equation.
• Chapter 8. Causal Structure.
• Chapter 9. Singularities.
• Chapter 10. The Initial Value Formulation.
• Chapter 11. Asymptotic Flatness.
• Chapter 12. Black Holes.
• Chapter 13. Spinors.
• Chapter 14. Quantum Effects in Strong Gravitational Fields.
• Appendix D. Conformal Transformations.
• Appendix E. Lagrangian and Hamiltonian Foundations of Einstein's Equation.
• Appendix F. Units and Dimensions.

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