
Abstract 
1 
Introduction 
2 
Basic Notions 

2.1 
Isolated horizons 

2.2 
Dynamical horizons 
3 
Area
Increase Law 

3.1 
Preliminaries 

3.2 
Area increase law 

3.3 
Energy flux due to
gravitational waves 
4 
Black Hole Mechanics 

4.1 
Mechanics of weakly isolated
horizons 

4.2 
Mechanics of dynamical horizons 

4.3 
Passage of dynamical horizons
to equilibrium 
5 
Applications in Numerical Relativity 

5.1 
Numerical computation
of black hole mass and angular momentum 

5.2 
Initial data 

5.3 
Black hole
multipole moments 

5.4 
Waveform extraction 
6 
Applications in Mathematical
Physics 

6.1 
Beyond Einstein–Maxwell theory 

6.2 
Structure of colored, static
black holes 
7 
Applications in Quantum Gravity 

7.1 
Preliminaries 

7.2 
Quantum
horizon geometry 

7.3 
Entropy 
8 
Outlook 
9 
Acknowledgements 

References 

Footnotes 

Figures 