In mathematics, K-theory is, firstly, an extraordinary cohomology theory which consists of topological K-theory. It also includes algebraic K-theory. It spans the subjects of algebraic topology, abstract algebra and some areas of application like operator algebras and algebraic geometry. It leads to the construction of families of K-functors, which contain useful but often hard-to-compute information.
In physics, K-theory and in particular twisted K-theory have appeared in Type II string theory where it has been conjectured that they classify D-branes, Ramond-Ramond field strengths and also certain spinors on generalized complex manifolds. For details, see also K-theory (physics).