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.