  We prove the existence of canonical scrolls; that is, scrolls playing the
role of canonical curves. First of all, they provide the geometrical version of
Riemann Roch Teorem: any special scroll is the projection of a canonical scroll
and they allow to understand the classification of special scrolls in P3.
Canonical scrolls correspond to the projective model of canonical geometrically
ruled surfaces over a smooth curve. We also prove that the generic canonical
scroll is projectively normal except in the hyperelliptic case and for very
particular cases in the nonhyperelliptic situation.
