in mathematics, a two-parameter family of curves in the plane or in space that are linear functions of the parameters. Suppose F₁, F₂, and F₃ are functions of two variables and none of the functions is a linear combination of the other two. The family of curves in the plane that are determined by the equation

(*) λ₁F₁ + λ₂F₂ + λ₃F₃ = 0

for all possible values of the parameters λ₁, λ₂, and λ₃ (except for the case λ₁ = 0, λ₂ = 0, and λ₃ = 0) constitutes a bundle. Equation (*) is in fact a function of two parameters—that is, of the two ratios λ₁: λ₂: λ₃. In addition, it is immediately apparent that the parameters occur in this equation linearly. The equation of a bundle of surfaces in space is formed analogously. The three equations F₁ = 0, F₂ = 0, and F₃ = 0 yield three elements of the bundle (three curves of three surfaces), which determine the entire bundle.

Bundles are usually considered whose elements are similar in certain respects; examples are a bundle of circles and a bundle of planes. We sometimes also speak of a bundle of lines in space; although the bundle is considered in space, its elements are curves rather than surfaces. Nevertheless, this case can be reduced to the case of a bundle of planes, since the pairwise intersections of elements of a bundle of planes determine a set of lines. In projective geometry, a bundle is understood to mean both sets—lines and planes—at once.