Basic concepts: Finite incidence structures; Incidence preserving maps; Incidence matrices; Geometry of finite vector spaces. Designs: Combinatorial properties; Embeddings and extensions; Automorphisms of designs; Construction of designs. Projective and affine planes: General results; Combinatorics of finite planes; Correlations and polarities; Projectivities. Collineations of finite planes: Fixed elements and orders; Collineation groups; Central collineations; Groups with few orbits. Construction of finite planes: Algebraic representations; Planes of Type IV, V ad Types I and II. Inversive planes: General definitions and results; Combinatorics of finite inversive planes; Automorphisms; The known finite models. Appendices: Associations schemes and partial designs; Hjelmslev planes; Generalized polygons; Finite semi-planes. Bibliography. Dictionary. Special notations. Index