I know of some earlier references to work by Hjelmslev on his "natural
geometry".
1898. (Hjelmslev=Petersen). Nouveau principe pour e/tudes de ge/ome/tries
des droites. Kgl. Danske Vid. Selsk. Forhandl. 283-344.
1907. Neue Begru"ndung der ebenen Geometrie. Math. Annalen 64, 449-474.
1909. Sur les principes fondamentaux de la ge/ome/trie. This is a conference
made at the Congre\s International des Mathe/maticiens in Stockholm.
Mentioned earlier:
1916. Die Geometrie der Wirklichkeit. Acta Math. 40 33-66 (I should have a
copy somewhere).
1923. Die natu"rliche Geometrie. Abh. Math. Sem. Univ. Hamburg, 2, 1-36.
1929-1949. Einleitung in die algemeine Kongruenzlehre. I-VI. Dansk Vid.
selsk. Math. Fys. Med. I:8(1929), II:10 (1929), III:19 (1942), IV and V: 22
(1945) pages?, VI:25 (1949), pages?
1940. La ge/ome/trie sensible. L'Enseignement Mathe/matique. 38, 7-27 and 38,
294-322 (I should have a copy somewhere).
As I remember, Hjelmslev finds that our usual (euclidean) points are not
very natural. Bigger points are more natural. It should be allowed that
more than one point passes through two points. Also, coordinates restricted
to the integers are natural. A personal comment: this is indeed close to
present day needs in which euclidean geometry is discretized and the reals
replaced by the integers.
Hjelmslev was followed in geometric developments in various directions. One
is ring geometry. Another is axiomatic (again in various ways). There are
developments in the direction of Tits' theory of buildings.
A place where to find references is the Handbook of Incidence Geometry
edited by me and published by North Holland, 1995, Amsterdam. It includes a
chapter on ring geometry by F.D.Veldkamp.
There is a bibliography by Artmann e.a. in Journ. Geometry, 7, 1976, 175-191.
With best wishes,
Francis Buekenhout