| 1 | Introduction | 1 |
| 2 | Bracket Polynomial, Temperley-Lieb Algebra | 5 |
| 3 | Jones-Wenzl Projectors | 13 |
| 4 | The 3-Vertex | 22 |
| 5 | Properties of Projectors and 3-Vertices | 36 |
| 6 | [theta]-Evaluations | 45 |
| 7 | Recoupling Theory Via Temperley-Lieb Algebra | 60 |
| 8 | Chromatic Evaluations and the Tetrahedron | 76 |
| 9 | A Summary of Recoupling Theory | 93 |
| 10 | A 3-Manifold Invariant by State Summation | 102 |
| 11 | The Shadow World | 114 |
| 12 | The Witten-Reshetikhin-Turaev Invariant | 129 |
| 13 | Blinks [actual symbol not reproducible] 3-Gems: Recognizing 3-Manifolds | 160 |
| 14 | Tables of Quantum Invariants | 185 |
| Bibliography | 290 |
| Index | 295 |