Generalized geometry lectures on type II backgrounds
  The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some past and recent results on the generalized complex structure of supersymmetric type II vacua in various dimensions. 
Dimitrios Tsimpis
hep-th math.DG