Intersection theory assigns a signed count to the intersection of subvarieties in an ambient algebraic variety. Bezout's theorem is the prototype: two curves of degrees d and e in ℙ² intersect in exactly d·e points, counted with multiplicity and over the algebraic closure. A tangency counts as a double point; intersections at infinity are included. The intersection product makes the Chow ring A*(X) into a graded ring, with cup product corresponding to intersection of cycles. On a surface, the self-intersection number C·C of a curve C measures how the curve can be deformed — the adjunction formula relates it to genus: 2g-2 = (K+C)·C. Intersection numbers are the fundamental numerical invariants computed in Gromov-Witten theory and enumerative geometry.