the hierarchy starting with principal bundles than sheaves. Bundle gerbes have been used in gauge theory and also string theory. Current work by others is developing a theory of non-abelian bundle gerbes. See also Twisted sheaf Azumaya algebra Twisted K-theory Algebraic stack Bundle gerbe String group References . . External links Introductory articles Constructions with Bundle Gerbes - Stuart Johnson An Introduction to Gerbes on Orbifolds, Ernesto Lupercio, Bernado Uribe. What is a Gerbe?, by Nigel Hitchin in Notices of the AMS Bundle gerbes, Michael Murray. Gerbes in topology Homotopy theory of presheaves of simplicial groupoids, Zhi-Ming Luo Twisted K-theory Twisted K-theory and K-theory of bundle gerbes Twisted Bundles and Twisted K-Theory - Karoubi Applications in string theory Stable Singularities in String Theory - contains examples of gerbes in appendix using the Brauer group Branes on Group Manifolds, Gluon Condensates, and twisted K-theory Lectures on Special Lagrangian Submanifolds - Very down-to earth introduction with applications to Mirror symmetry The basic gerbe over a compact simple Lie group - Gives techniques for describing groups such as the String group as a gerbe Homological algebra Sheaf theory