| 1 | Learn the concept of homotopy and its applications. |
| 2 | Learn the concept of homotopy type. |
| 3 | Learn the concepts of curves, fundamental groups, and homotopy groups. |
| 4 | Learn the concept of linear subspaces of Euclidean space. |
| 5 | Learn the concepts of simplices and the orientation of simplices |
| 6 | Learn the concept of simplicial complexes |
| 7 | Learn the concepts of touch, triangulation, and examples of triangulation |
| 8 | Learn the concept of finitely generated abelian groups |
| 9 | Learn the concepts of chains, limits, and cycles |
| 10 | Learn the concept of homology groups |
| 11 | learning the concept of Betti numbers |
| 12 | learning the concept of chains on an arbitrary abelian group |
| 13 | learning the concept of cohomology groups |
| 14 | learning the sustainable properties of these definitions and concepts given in algebraic topology and their contributions to development |