| 1 | The Basic Spaces and upper half-plane model | [1] p. 1-7 |
| 2 | The Riemann Sphere and The Boundary at Infinity of upper half-plane | [1] p. 8-22, [3] p. 22-27 |
| 3 | The Group of Möbius Transformations | [1] p. 23-29, [3] p. 41-49 |
| 4 | Transitivity Properties and Cross Ratio | [1] p. 30-38, [3] p. 60-67 |
| 5 | Classification of Möbius Transformations and A Matrix Representation of a Möbius transformation | [1] p. 39-47 |
| 6 | Reflections, The Conformality of Möbius Transformations | [1] p. 48-55 |
| 7 | Preserving of upper half-plane and The Structure of Topological group | [1] p. 56-62, [2] p.60-62, [5] p. 95-112 |
| 8 | Properties of Topological groups | [5] p. 95-112 |
| 9 | Topological transformation groups | [5] p.143-152 |
| 10 | The group PSL(2,IR) and its discrete subgroups | [2] p. 217-220, [4] p.23-31 |
| 11 | Hyperbolic distance and hyperbolic length in upper half-plane | [1] p. 73-88, [2] p. 221-227, [3] p. 144-148 |
| 12 | Hyperbolic Polygons, Hyperbolic Area and the Gauss?Bonnet Formula | [1] p. 154-174, [4] p.11-14 |
| 13 | Trigonometry in hyperbolic plane and its relation with sustainability. | [1] p. 181-189, [3] p. 144-149, [4] p.15-18 |
| 14 | Fuchsian groups and their algebraic properties | [2] p. 231-239, [4] p.15-18 |