| 1 | Ability to learn the concepts of the hyperbolic plane model, the Riemann sphere, and the boundary at infinity of the upper half-plane. |
| 2 | Ability to learn Group of Möbius Transformations and their properties |
| 3 | Ability to learn concepts of classification of Möbius Transformations, Matrix Representation, Reflections, Conformality, Preserving of upper half-plane |
| 4 | Ability to learn Topological groups, Topological transformation groups and their properties |
| 5 | Ability to learn the concepts of hyperbolic distance, hyperbolic length and hyperbolic area in upper half-plane |
| 6 | Ability to learn the group PSL(2,IR) and its discrete subgroups and algebraic properties |