ABSTRACT
The study of Differential Geometry usually starts with that of curves in the plane and space. The reasons for doing this are multiple and evident: Historically, Differential Geometry evolved, in parallel with Calculus (or rather like a branch of it), beginning thus from Newton; thus, it concerned itself, in the beginning with planar curves. Their study gives the impetus and first directions for the study of surfaces; thus, the understanding of the geometry of curves is necessary for that of surfaces (thence of higher dimensional manifolds as well). Also, on a didactic level, it is traditionally deemed necessary to encourage students by gently introducing them to the subject, via the simplest case, i.e. that of curves. Strangely enough, students do not tend to respond positively to this approach, as they find it tedious and perceive that the time dedicated to this first chapter is far longer than it truly is.
