This course is an introduction to Einstein's theory of gravity, i.e., the General Relativity. The content will include:
(1) Basics of special relativity. 4-dimensional Minkowski spacetime. Lorentz group. Poincare group.
(2) Basics of differential geometry. Manifolds. Vectors. Tensors. Differential forms. The metric. Connections. Curvatures.
(3) The Equivalence principle. Gravity as geometry. Einstein's field equations. Lagrangian formulation.
(4) The Schwarzschild metric. Geodesics of Schwarzschild. Experimental tests.
(5) Black hole. Event horizons. Kruskal coordinates.
(6) Gravitational wave solutions.
(7) Cosmology. Robertson-Walker metrics. gravitational lensing.