  Generalized complex geometry, introduced by Hitchin, encompasses complex and
symplectic geometry as its extremal special cases. We explore the basic
properties of this geometry, including its enhanced symmetry group, elliptic
deformation theory, relation to Poisson geometry, and local structure theory.
We also define and study generalized complex branes, which interpolate between
flat bundles on Lagrangian submanifolds and holomorphic bundles on complex
submanifolds.
