ABSTRACT
This chapter deals with the basic geometric properties of curves in three dimensional Euclidean space and provides the necessary mathematical background from geometry and analysis. The topics include the parametric representation of curves, the arc length of a curve as its natural parameter, the geometric principles and construction of important planar curves, the frame of curves, Frenet's formulae, the curvature and torsion of curves and their geometric significance, the characteristic shape of a curve in a neighbourhood of any of its points osculating circles and spheres, involutes and evolutes of curves, the fundamental theorem of curves, the natural or intrinsic equations of curves, lines of constant slope, and spherical images of curves.
