Courant algebroids and generalized complex geometry

Abstract

In this survey, we recall the background and major developments in Courant algebroids and their applications. We mainly recall the origin and motivation of the definition of Courant algebroids. A brief introduction to the theories of Dirac structures, Lie bialgebroids, the Clifford construction, spinor representation, generalized complex geometry and regular Courant algebroids are given.