  In recent work N. Hitchin introduced the concept of "generalised geometry".
The key feature of generalised structures is that that they can be acted on by
both diffeomorphisms and 2-forms, the so-called $B$-fields. In this lecture, we
give a basic introduction and explain some of the fundamental ideas. Further,
we discuss some examples of generalised geometries starting from the usual
notion of a Calabi-Yau manifold, as well as applications to string theory.
