Course

Einstein equations, Bianchi identity, Conservation laws, Energy conditions, Linearized gravity

Energy-momentum conservation, Born-Infeld theory, Einstein-Hilbert action, Lovelock theorem

Particles and matter in curved spacetime, Geodesic deviation equation, Energy momentum tensor

Killing vectors, Curvature, Riemann family, Bianchi identity & Einstein tensor

Covariant derivative, Metric, Equivalence principle, Invariant volume element, Parallel transport

Tensors, Tensor algebra, Differentiating tensors, Connection

Gravitational redshift again, Field theory for gravity, Manifolds

Freely falling frame, Geodesic equation, Curved metric, Rindler space, Newtonian limit

Nambu-Goto and Polyakov actions, Einstein's path to GR, Einstein's elevator, Gravitational redshift

Introduction (with the participation of Rob Spekkens!) and mathematical prerequisites.

Special Relativity: Spacetime and causal structure, Lorentz transformations, Relativistic particle