Advanced Lectures on General Relativity

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.