If X is a topological space with involution, we can use Atiyah's Real vector bundles to define analogues of the Witt group and Brauer-Wall groups in algebra. They are easier to compute than their algebraic cousins, because they are  finitely generated and related to Borel cohomology.  If V is an algebraic variety defined over the real numbers, the Brauer-Wall group of V is the direct sum of the Real graded Brauer group of the associated space with involution and a divisible group; they are isomorphic if V is smooth projective and the Hodge number h^{0,2} is zero.