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.

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.