
Abstract 
1 
Introduction 
2 
Quantum Gravity: Where Are We? 

2.1 
What is the
problem? The view of a highenergy physicist 

2.2 
What is the problem?
The view of a relativist 

2.3 
Strings and loops 
3 
The Development of Loop
Gravity 
4 
Resources 
5 
Ideas and Physical Inputs 

5.1 
Quantum field theory on a
differentiable manifold 

5.2 
Why loops? 

5.3 
Physical meaning of diffeomorphism
invariance and its implementation in the quantum theory 

5.4 
Problems not
addressed 
6 
Formalism 

6.1 
Classical theory 

6.2 
Quantum kinematics 

6.3 
Loop
and spin network states 

6.4 
Diffeomorphism invariance 

6.5 
Other structures in


6.6 
Dynamics: I. Hamiltonian 

6.7 
Dynamics: II. Spin foams 

6.8 
Dynamics:
III. Group field theory 

6.9 
Matter couplings 

6.10 
Variants: fundamental
discreteness 
7 
Physical Results 
8 
Open Problems and Current Lines of
Investigation 
9 
Short Summary and Conclusion 
10 
Acknowledgments 

References 

Footnotes 

Figures 