We introduce the basic cmcepts of differential geometry, focus it on the notion of curvature.
1. curvature of plane curves.
2. curvature of space curves.
3. curvature of sunfaces ( lyip in IR3 ) : principal cinvatine, Gauss curvature, mean curvature.
4. Innate curvature: Gauss theorema Egregium.
5. Curvate and global geanetry: Gauss- Bonnet theorem.
6. Conclusion: Non-Euclidean geometry, abstract sunfaces, and manifolds.