
Abstract

1

Introduction

2

Quantum Gravity: Where are We?


2.1

What is the ...


2.2

What is the ...


2.3

Strings or loops?

3

History of Loop Quantum Gravity, Main Steps

4

Resources

5

Main Ideas and Physical Inputs


5.1

Quantum field theory ...


5.2

One additional assumption


5.3

Physical meaning of ...


5.4

Problems not addressed

6

The Formalism


6.1

Loop algebra


6.2

Loop quantum gravity


6.3

Loop states and ...


6.4

Relation between spin ...


6.5

The representation


6.6

Algebraic version (``loop ...


6.7

Other structures in ...


6.8

Diffeomorphism invariance


6.9

Dynamics


6.10

Unfreezing the frozen ...

7

Physical Results


7.1

Technical


7.2

Physical

8

Main Open Problems and Main Current Lines of Investigation

9

Short Summary and Conclusion


9.1

Conclusion

10

Acknowledgments
