Finite geometry is the study of finite incidence structures (or hypergraphs) satisfying certain geometrically motivated axioms. In this course we will introduce various finite geometries and explore how these structures interact with combinatorics. In particular, we will study finite projective and affine spaces, generalized polygons and polar spaces. On the combinatorial side we will discuss blocking sets, strongly regular graphs, finite field Kakeya and Nikodym problems, and the cage problem.

Finite Geometry and Combinatorial Applications by Simeon Ball

An Introduction to Incidence Geometry by Bart De Bruyn 

Combinatorics of finite geometries by Lynn Margaret Batten. 

Incidence Geometry by G.~Eric Moorhouse

Projective Geometr' by Rey Casse

Algebraic Graph Theory by Chris Godsil and Gordon Royle