ABSTRACT
If we were to deal completely with all geometries admitting transitive actions, we would need to double the size of this book. For example, one could consider group actions on affine planes, projective planes, parallelisms of projective spaces, partial parallelisms of projective spaces, actions on projective spaces or affine spaces, on Steiner triple systems, on general designs and so on. We necessarily need to restrict our remarks here to include results that impinge most directly on translation planes, even if this becomes quite subjective. So, we shall mainly focus directly on affine and projective planes and their interconnections when considering the myriad problems considering transitive actions on geometries.
