Curves in the plane and in space, tangent line to a curve, arclength-natural parameter, Frenet’s moving frame, curvature and torsion, generalized helices, the fundamental theorem of space curves, global theory of curves, isoperimetric inequality, regular surfaces, construction of regular surfaces using the implicit function theorem, tangent plane, first and second fundamental form, surface area, Gauss map, shape operator (Weingarten map), normal curvature, principal curvatures, Euler’s formula, Gauss curvature, mean curvature, Theorema Egregium.