Topological structures in string theory

In string theory space-time comes equipped with an additional geometric str ucture called a B-field or 'gerbe'. I describe this structure, mention its relationship with noncommutative geometry, and explain how to use the B-fie ld to define a twisted version of the K-theory of space-time. String-theore tical space-time can contain topologically non-trivial dynamical structures called D-branes. These are simply accounted for in the framework of confor mal field theory. In a highly simplified limiting case-topological field th eory with a finite gauge group - the D-branes naturally represent elements of the twisted K-theory of space-time: the K-theory class is the 'charge' o f the D-brane.