1. Introduction to the Course
2. Relativity and Symmetry
3. Symmetry Transformations and Metrics 2 Case Studies
4. Spacetimes, SO(1,3), Spacetime Diagrams and Causality
5. Index Notation and a Pinch of Vectors
6. Vectors and Dual Vectors
7. Tensors
8. Relativistic Kinematics and Dynamics
9. Densities
10. Equivalence Principles
11. Manifolds
12. Tensors Under General Coordinate Transformations
13. Loose Ends, Metrics, Flatness and LICs
14. A New Hope (Derivative)
15. Interpreting Christoffel Symbols and Parallel Transport
16. Geodesics
17. Curvature
18. Symmetries, Killing Vectors and Maximally Symmetric Spaces
19. General Relativity and Gauge Theories
20. Where's Newton?
21. The Schwarzchild Solution
22. Geodesics of Schwarzchild and Tests of General Relativity
23. Interior Solutions and Stellar Collapse
24. Schwarzchild Black Holes
25. Maximally Extended Geometries
26. Rotating Black Holes
27. Black Hole Thermodynamics
28. Gravitational Waves
29. FRW Cosmologies
30. Our Universe

This course will develop and apply Einstein's General Theory of Relativity. One of the most interesting aspects of this subject is that it brings the student to our modern understanding of the earliest recognized of the fundamental forces of nature, i.e. gravitation. The student sees this first as a source of constant acceleration near the surface of the Earth (projectile motion), and then matures their understanding, with Newton's Universal Law of Gravitation, to a notion of gravitation as a central force acting between any two bodies with nozero mass. While the Newtonian view works in many applications, it fails when contemplating systems that are ginormously massive. The (more) correct theory, General Relativity, is not a simple "extension" of Newtonian gravity, but rather a complete revision of our understanding of gravity. In some cases, e.g planetary orbits, the predictions of General Relativity provide small corrections to the "for the most part correct" results of the Newtonian theory. However in other circumstances, e.g. black holes and cosmology, General Relativity gives us results that quite honestly would have sent Newton running scared and have left many other physicists scratching their heads in disbelief!

This subject is often tauted as too mathematically sophisticated for undergraduates, which I find to be a shame since the concepts underlying the theory can be expressed concisely and clearly given a reasonable effort on the part of the instructor. While the subject does involve mathematics that extend beyond what has already been encountered in most other physics courses, the truth of the matter is that it really boils down to taking what you already know and being as general as possible with it. When you leave this course, you will know far better what a "vector" is than many professional physicists. There is a wealth of material that we can study and the extent of what we do will rely in part on your diligence to the course.