These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are:

Surface charges as conserved quantities in theories of gravity;
Classical and holographic features of three-dimensional Einstein gravity;
Asymptotically flat spacetimes in four dimensions: BMS group and memory effects;
The Kerr black hole: properties at extremality and quasi-normal mode ringing.

Each topic starts with historical foundations and points to a few modern research directions.

�ber die Autorin bzw. den Autor

Geoffrey Comp�re is a FNRS Research Associate at the Universit� Libre de Bruxelles, Belgium. His research, as a theoretical physicist, focuses on surface charges in gravitation, the physics of black holes close to extremality, supergravity and infinite-dimensional symmetries, topics on which he has authored over 50 papers. He developed the package SurfaceCharges for Mathematica which allows to compute surface charges in gravitation coupled to matter. He is the recipient of an ERC Starting Grant addressing the holographic properties of black holes. As a member of the LISA consortium and of the Belgian Gravitational Wave Center, he is currently developing waveform models to confront General Relativity with upcoming high-precision gravitational wave observations.

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