The equivalence principle and the principle of general covariance.
Curved manifolds (spaces): metric, connection, parallel transport, curvature, etc.
Physics in curved space-time: particle dynamics, electromagnetism, hydrodynamics, etc.
The Einstein equation. Solutions: black holes, gravitational waves, cosmology, etc.
The quantum vacuum, Unruh and Hawking radiation.
Analogues of gravity and their applications.