This chapter is devoted to ruled surfaces. A one-parameters smooth manifold of lines — we could say we take a line and move it around — traces out a smooth surface in space. We first study the subject from the viewpoint of projective differential geometry by discussing the distribution of tangent planes. It turns out that there are the classes of skew and torsal surfaces which exhibit a totally different tangent behaviour. The latter will be treated in a chapter of their own (see Chap. 6). In Sec. 5.2, we look at algebraic ruled surfaces and especially at rational ones. An enumeration and projective classification of low degree surfaces on the one hand leads to interesting specimens, and on the other hand shows some kinds of typical behaviour by means of simple examples. The third part of this chapter deals with the Euclidean differential geometry of ruled surfaces. This is in some aspects similar to the classical theory of space curves, which is only to be expected from an inherently one-dimensional object. Finally we show how to deal with ruled surfaces in numeric computations, and how to solve approximation and interpolation problems concerned with them.