ABSTRACT
When considering a graph G, a diagram of G is often drawn (in the plane). Sometimes no edges cross in a drawing, while on other occasions some pairs of edges may cross. Even if some pairs of edges cross in a diagram of G, there may very well be other drawings of G in which no edges cross. On the other hand, it may be impossible to draw G without some of its edges crossing. Even if this should be the case, there is a variety of other surfaces on which we may attempt to draw G so that none of its edges cross. This is the subject of the current chapter.
