Generalized geometry is a unifying approach to geometric structures where, for
example, complex and symplectic structures become particular instances of a more
general structure: a generalized complex structure. After a selfcontained
introduction to generalized complex geometry (which is only possible for
evendimensional manifolds), I will explain how generalized geometry can be upgraded
to Bngeneralized geometry, in which the generalizedcomplex approach applies as well
to odd dimensions. Finally, I will comment on some ongoing joint work with J. Porti in
which we look at the case of threemanifolds.
