| 1 | The acqusition of the mathematical skills in topics, such as differential geometry, Cartan’s structure equations, exterior algebra, differential forms and their applications to theories in physics |
| 2 | The acqusition of some technical skills in scalar-tensor gravity theories, variaitonal principles, equivalent lLgrangians, conformal transformations |
| 3 | The acqusition of technical skills in the Einstein-Maxwell’s theory in 3+1 spactime dimensions |
| 4 | The acqusition of technical skills in geodesic equation in 4+1 spacetime dimensions and Kaluza ansatz |
| 5 | The reudction of 4+1 dimensional gravitational theory to 3+1 spacetime gravity and electromagnetism on a circle. |
| 6 | The acqusition of skills on the reduction mechanism on different compact manifolds with some conformal scalar fields |
| 7 | The acqusition of skills on successive reduction of gravitational models on a torus |
| 8 | The acqusition of skills in higher dimensional cosmological models and Kaluza-Klein ansatz |
| 9 | The acqusition of general technical skills in the reduction of n+1 dimensional models gauge fields to 3+1 dimensions and unified theories |
| 10 | The acqusition of technical skills in Lie groups and their geometrical properties |
| 11 | The acqusition of the theory of Fiber bundles, connection and curvature defined on a frame bundle |