| 1 | Review of Concepts | 3 |
| 1.1 | Theory of Quadratic Polynomials | 3 |
| 1.2 | Dense Hyperbolicity | 6 |
| 1.3 | Steps of the Proof of Dense Hyperbolicity | 12 |
| 2 | Quasiconformal Gluing | 25 |
| 2.1 | Extendibility and Distortion | 26 |
| 2.2 | Saturated Maps | 30 |
| 2.3 | Gluing of Saturated Maps | 35 |
| 3 | Polynomial-Like Property | 45 |
| 3.1 | Domains in the Complex Plane | 45 |
| 3.2 | Cutting Times | 47 |
| 4 | Linear Growth of Moduli | 67 |
| 4.1 | Box Maps and Separation Symbols | 67 |
| 4.2 | Conformal Roughness | 87 |
| 4.3 | Growth of the Separation Index | 100 |
| 5 | Quasiconformal Techniques | 109 |
| 5.1 | Initial Inducing | 109 |
| 5.2 | Quasiconformal Pull-back | 120 |
| 5.3 | Gluing Quasiconformal Maps | 129 |
| 5.4 | Regularity of Saturated Maps | 133 |
| 5.5 | Straightening Theorem | 139 |
| Bibliography | 143 |
| Index | 147 |
