The following pages contain descriptions of the linear spaces on at most nine points. For each linear space, we give a picture, the number of lines, the collineation group acting on the space (this appears in a box) and the number of point orbits under this group.

We use the following group theoretic notations for the collineation groups:

Cn is the cyclic group of order n,

Sn is the symmetric group on n letters,

D2n is the dihedral group of order 2n,

пiH is the direct product of / groups H,

ΣiH is the direct sum of / groups H,

Gn is a group of order n.

The general notation G is used when the group is not describable as a direct sum or product of the cyclic, symmetric or dihedral groups.

We wish to thank Jean Doyen, who, with much time and effort, compiled this comprehensive table for us and offered to let us use it as an appendix to this monograph. Any errors in it are due to the present authors.