  These are the lecture notes from the 26th Winter School "Geometry and
Physics", Czech Republic, Srni, January 14 - 21, 2006. These lectures are an
introduction into the realm of generalized geometry based on the tangent plus
the cotangent bundle. In particular we discuss the relation of this geometry to
physics, namely to two-dimensional field theories. We explain in detail the
relation between generalized complex geometry and supersymmetry. We briefly
review the generalized Kahler and generalized Calabi-Yau manifolds and explain
their appearance in physics.
