The original main part of this book was just a sequel to the Montreal Notes 3 . The main part was the proof to the Theorem (36.9), namely that All irreducible nonsingular space curves of degree at most five and genus at most one over an algebraically closed ground field are complete intersections. As such, the Theorem was completely proved in 1971. Two versions of the proof have been written and circulated, but none published. We intended to give a completely
self-contained treatment of the Theorem, and in the process, the size of the proof, or rather, the preparatory material, enlarged; while the proof continued to become clearer and somewhat sharper. The present version was finally started in June 1973, and we finally 'decided that
it had to be a book.