General Relativity

General relativity is the theory of the structure and dynamics of spacetime. These lecture notes provide an introduction into the concepts of differential geometry, in particular pseudo-Riemannian geometry, and discusses the ideas behind the construction of a gravitational field equation. Exact solutions to the field equation for highly symmetric spacetimes, i.e. black holes, FLRW cosmologies and gravitational waves, are worked out. Advanced topics that are covered include Lie derivatives and the Killing equation, the derivation of the field equations from variational principles, and the formulation of field theories on curved spacetimes.