| 1 | teaching the concept of homotopy, Understanding the applications on the homotopy |
| 2 | teaching the concept of homotopy type |
| 3 | teaching the concepts of the main groups and homotopy groups, curves |
| 4 | teaching simplex and the concepts of direction in Simplexes, the concept of simplicial complexes |
| 5 | touching, teaching the concepts of triangulation, gaining solving skills examples of triangulation |
| 6 | teaching the concepts of borders, chain and cycle, the concept of homology groups |
| 7 | teaching the concept of calculation of homology groups and making application |
| 8 | increase their knowledge and skills, narration, understanding to gain the ability to interpret |
| 9 | Teaching the contribution of sustainable features of these definitions and concepts given in algebraic topology to development |