A few weeks ago, I attended a wonderful talk about the real projective plane by Bruce Cohen and David Sklar. This reminded me that 40 years ago, or so, I wrote an MA thesis at UC Berkeley on Topics in finite projective geometry. I just scanned it and uploaded it to my Web site on the off chance someone would be interested.
The thesis consisted of a review of some of the literature about non-Desarguesian projective geometries. The most memorable part was about a sort of reverse analytic geometry, where you start with a geometry and construct an algebraic system in it, using geometric definitions for addition and multiplication. Interestingly, whether certain geometric theorems hold in that geometry corresponds to whether the algebraic structure is a field.