  This thesis starts with a review of BPS M-branes and their supergravity
solutions. These solutions can be obtained in various ways. We describe the
harmonic function rule and the Fayyazuddin-Smith metric ansatz in detail,
illustrating both methods by examples of M-branes wrapping holomorphic curves.
Another, simpler way, is to use calibrations. In order for a wrapped brane to
be BPS, the cycle it wraps must be calibrated; given the relevant calibration,
there exists a procedure which yields the supergravity solution almost
immediately. In the past, this method was applied only to Kahler calibrations,
as these were the only ones known to exist in backgrounds with non-trivial
flux. We extend this method to a wider domain, using a constraint to classify
possible calibrations. A rule is given which can generate the required
constraint for any given M-brane wrapped on a holomorphic cycle. Ways in which
this constraint can be satisfied are also discussed.
