• The student understands the fundamental ideas underlying the construction of General Relativity and their conceptual and phenomenological consequences.
• The student is familiar and can work with the most important tensors appearing in General Relativity (metric tensor, curvature tensors, stress-energy tensor).
• The student knows the geodesic equation and can solve it in simple cases.
• The student is familiar with Einstein’s equations and its most important solutions including Friedmann-Robertson-Walker cosmology, linearized gravitational waves, and the Schwarzschild metric.
• The student has a basic idea of how to solve Einstein’s equations using suitable, simplifying ansätze for the spacetime metric and the stress-energy tensor.

About 100 years after its first proposal, Einstein’s theory of general relativity is entering into a new exciting phase: astrophysical measurements have entered into a stage of precision cosmology where observations start to rule out cosmological models. Moreover, the first direct detection of gravitational waves in 2015 has opened a new window for exploring the physics of the early universe. The course uses a “physics first” approach laying the foundations for understanding these developments based on first principles. In this way it touches on a wealth of frontier scientific topics including curved spacetime, black holes, gravitational waves, and cosmology.