  In these lectures we review Generalized Complex Geometry and discuss two main
applications to string theory: the description of supersymmetric flux
compactifications and the supersymmetric embedding of D-branes. We start by
reviewing G-structures, and in particular SU(3)-structure and its torsion
classes, before extending to Generalized Complex Geometry. We then discuss the
supersymmetry conditions of type II supergravity in terms of differential
conditions on pure spinors, and finally introduce generalized calibrations to
describe D-branes. As examples we discuss in some detail AdS4
compactifications, which play a role as the geometric duals in the
AdS4/CFT3-correspondence.
