1. Differential Geometry (Approximately 3 weeks)

    1. Manifolds, Charts, Functions
    2. Tangent Vectors, Cotangent Vectors, Tensors
    3. The Gradient
    4. Covariant Derivatives
    5. Curvature

  2. Special Relativity (Approximately 3 weeks)

    1. Postulates
    2. Invariance of the Line Interval
    3. Lorentz Transformations
    4. Relativistic Kinematics
    5. Acceleration

  3. General Relativity (Approximately 3 weeks)

    1. Einstein’s Equations
    2. Symmetries and Conservation Laws
    3. Initial-Value Formulation

  4. Relativistic Stars (Approximately 3 weeks)

    1. Spherical Stellar Models
    2. Rotation Stellar Models
    3. Stability Theory

  5. Black Holes (Approximately 3 weeks)

    1. Spherical Black Holes
    2. Rotating Black Holes
    3. Particle Orbits around Black Holes
    4. Analytic Extensions
    5. Stability Theory

  6. Current Research Topics - (Intermingled with above as time permits)