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:

1. 
   

   Surface charges as conserved quantities in theories of gravity;

   
   


2. 
   

   Classical and holographic features of three-dimensional Einstein gravity;

   
   


3. 
   

   Asymptotically flat spacetimes in four dimensions: BMS group and memory effects;

   
   


4. 
   

   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.