  For later use in subsequent upcoming arxiv.org prepublications, basic
foundational material on local, smooth or real analytic, CR-generic
submanifolds of complex Euclidean spaces is developed from scratch, with strong
emphasis on the interplay between extrinsic and intrinsic aspects, a
constructive option that commands to perform computational syntheses in
coordinates. Mainly, one finds a self-contained proof of the existence of
precisely six general classes: I, II, III-1, III-2, IV-1, IV-2 of nondegenerate
general CR manifolds up to dimension 5, class III-2 being unobserved untill
now.
