| 1 | To introduce concept of differentiable manifold and differentiable maps |
| 2 | To introduce concept of vector fields on manifolds, integral curves, Lie bracket, forms on differentiable manifold |
| 3 | To introduce Riemannian manifold, Riemannian Connection , LC koneksiyonunu |
| 4 | To introduce Riemann curvature, sectional curvature, Ricci curvature |
| 5 | To give information about induced connection on the submanifold, Gauss's equation |