We study projective surfaces of degree in projective -space, more precisely (non-conic) irreducible non-degenerate surfaces of degree . We may divide up the class of these surfaces in surfaces whose affine cone satisfies the second Serre property and surfaces which occur as almost non-singular projections of either a smooth rational scroll or else of a del Pezzo surfaces which is arithmetically Cohen-Macaulay. We focus on those surfaces which occur as almost non-singular projections and study their geometric and cohomological properties.