  These notes are based on lectures given at the Clay School on Geometry and
String Theory, Isaac Newton Institute, Cambridge, 25 March - 19 April 2002.
They attempt to provide an elementary and somewhat self contained discussion of
the construction of supergravity solutions describing branes wrapping
calibrated cycles, emphasising the geometrical aspects and focusing on D=11
supergravity. Following a discussion of the role of special holonomy
backgrounds in D=11 supergravity, the basic membrane and fivebrane solutions
are reviewed and the connection with the AdS/CFT correspondence is made. The
world-volume description of branes is introduced and used to argue that branes
wrapping calibrated cycles in special holonomy manifolds preserve
supersymmetry. The corresponding supergravity solutions are constructed first
in an auxiliary gauged supergravity theory which is obtained via Kaluza-Klein
reduction.
