I. Special relativity
Repetition of tensor notation. The meaning of relativity theory. Einstein's postulates. Geometry of the Minkowski space and Lorentz transformations. Length contraction and time dilation. The twin paradox and proper time. Energy and momentum in special relativity. Maxwell's equations and their relativistic covariance.
II. Basic differential geometry
Local coordinates on manifolds. Covariant and contravariant vectors and tensors. (Pseudo-)Riemannian metric. Covariant derivative (Levi-Civita connection and Christoffel symbols). Parallel transport. Curvature of spacetime.
III. General relativity
The principle of equivalence. Gravitational redshift and light deflection.
The Schwarzschild spacetime and experimental tests of general relativity.
Einstein's field equations. Introduction to cosmological models.