1. The Birth of General Relativity
2. Beyond Newtonian Gravity
3. Review of Relativistic Electrodynamics
4. Inertial Frames and the Principles of Equivalence
5. Geodesic Equation for Spacetime
6. Curvature of Spacetime
7. Uniqueness & Examples of Curvature Tensor
8. Obtaining Einstein’s Equations as Euler-Lagrange Equations
9. Freely-falling Frames & Physical Observations in a Metric
10. Conservation Laws and Killing Vectors
11. Vacuum Solutions of the Einstein Field Equations
12. Particle Motion in a Schwarzschild Metric
13. Massless Particles
14. Schwarzschild Black Holes
15. Properties of the Schwarzschild Black Hole
16. Properties of the Schwarzschild Black Hole II
17. Penrose Diagrams
18. The Copernican Principle
19. Solution to Einstein’s Static Universe
20. Evolving, Homogeneous, Isotopic Universe
21. Calculating the Age of the Universe
22. Cosmological Evolution in the Presence of a Scalar Field

Course DescriptionThis is a graduate course at the Tata Institute of Fundamental Research, Mumbai, intended primarily for students in the Department of Theoretical Physics.

Several textbooks will be used during the course. A list of textbooks on this subject can be found here or by visiting the links section:

One book I might end up following closely is ''General Relativity'' by Robert Wald. The list of contents of this book is a reasonable guide to what I intend to present in the course:
- Introduction
- Manifolds and Tensor Fields
- Curvature
- Einstein's Equation
- The Schwarzschild Solution
- Homogeneous, Isotropic Cosmology

Another textbook recommended is a friendly introduction to general relativity, called "Spacetime and Geometry" by Sean Carroll. It can be found under the Read Textbook button.