1. Holonomies and the group of loops; 2. Loop coordinates and the extended group of loops; 3. The loop representation; 4. Maxwell theory; 5. Yang-Mills theories; 6. Lattice techniques; 7. Quantum gravity; 8. The loop representation of quantum theory; 9. Loop representation: further developments; 10. Knot theory and physical states of quantum gravity; 11. The extended loop representation of quantum gravity; 12. Conclusions: present status and outlook; References; Index.