**J.C. Álvarez Paiva**

In this chapter we study the geometry of -dimensional projective space with special emphasis on the projective plane. We change somewhat our point of view and study the projective plane not only as a homogeneous space under an action of , but also as a space with a family of distinguished subspaces (the projective lines) that satisfy a number of incidence relations.

- Anything preceded by a * may be left for a second reading.
- Next to the exercises there is a two-digit number in parentheses which describes its degree of difficulty. The simplest exercises are identified by a (00), while the hardest -- those that could take you a week of intensive brain work -- are identified by a (50).

- Basic concepts
- Projective geometry vs. affine geometry
- The fundamental theorems
- Bibliography
- About this document ...

Juan Carlos Alvarez 2001-01-22