- Plane and space curves, examples. Arclenght parametrization, Frenet frame, Frenet formulas, curvature and torsion, evolutes and involutes.

- Parametrized surfaces, examples. Curves on surfaces. First fundamental form and its applications. Surface mapping (isometries, conformal mappings). Normal curvatures and second fundamental form. Principal directions and principal curvatures. Mean and Gaussian curvature, Theorema egregium, geodesic curves.

Basic course of classical differential geometry curves and surfaces.