In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Buildings were initially introduced by Jacques Tits as a means to understand the structure of isotropic reductive linear algebraic groups over arbitrary fields. The more specialized theory of Bruhat–Tits buildings (named also after François Bruhat) plays a role in the study of p-adic Lie groups analogous to that of the theory of symmetric spaces in the theory of Lie groups.