| 1 | To teach Space curves ,Frenet vectors, Frenet planes, curves and geometric meanings of curvatures |
| 2 | To introduce Circle of curvature, sphere of curvature , osculating sphere, spherical curves, slant lines,Involute, evolute, Bertrant curves and spherical indicators. |
| 3 | To teach of the concepts of the theory of surfaces and hypersurfaces.To teach Shape operator and the shape operator algebraic invariant. |
| 4 | To teach Gauss map and Weingarten map.To teach hypersurfaces types and properties of differentiable maps between them |