Part I : Curves :
 Curves : Parametrized and regular curves, arc length, parametrization by arc length.
 Local Theory : TangentNormalBinormal frame, curvature, torsion, fundamental theorems of local theory of plane and space curves.
 Global Theory : Simple curves, the Jordan curve theorem (without proof), isoperimetric inequality, the fourvertex theorem.
Part II : Surfaces :
 Surfaces : Parametrization, change of parameters, smooth functions, tangent plane, differential, diffeomorphism, inverse and implicit function theorems.
 Second Fundamental Form and Curvature : Gauss map, oriented surfaces, second fundamental form, Gauss, mean and principal curvatures, normal sections.
 Integration on Surface : Definition of integral, partitions of unity, change of variables formula, divergence theorem.
 Global Extrinsic Geometry : Positively curved surfaces, Minkowski formulas, Aleksandrov theorem, isoperimetric inequality.
 Intrinsic Geometry : Rigid motions and isometries, Gausss theorema egregium, geodesics, existence and uniqueness of geodesics, HopfRinows theorem.
 GaussBonnet theorem : Degree of maps between surfaces, index of a vector field at an isolated zero, GaussBonnet formula, Euler characteristic.
