This work is based on incidence structures. Incidence structure is an important term that is often used in various mathematical disciplines. At the beginning, we met with the pregeometry or incidence structure of the set I and presented the basic results that apply to the pregeometry. Then, we dened the incidence structure as a ordered triple which is consisted of two non-empty disjoint sets and incidence relation. The pregeometry of rank 2 over the set fpoint;lineg we associate with the incidence structure, and in the further work for the pregeometry of rank 2 over the set fpoint;lineg we use the corresponding incidence structures. In this way we have identied the pregeometry with the incidence structure. One class of incidence structures consists of projective and a¢ ne planes and spaces. We are particularly interested in the relationship between the projective and the affine planes. At the end of the work, we introduced concepts related to projective and affine planes on projective and affine spaces.