  We investigate the recently developed theory of multiple membranes. In
particular, we consider open membranes, i.e. the theory defined on a membrane
world volume with a boundary. We first restrict our attention to the gauge
sector of the theory. We obtain a boundary action from the Chern-Simons terms.
Secondly, we consider the addition of certain boundary terms to various
Chern-Simons theories coupled to matter. These terms ensure the full bulk plus
boundary action has the correct amount of supersymmetry. For the ABJM model,
this construction motivates the inclusion of a boundary quartic scalar
potential. The boundary dynamics obtained from our modified theory produce
Basu-Harvey type equations describing membranes ending on a fivebrane. The
ultimate goal of this work is to throw light on the theory of fivebranes using
the theory of open membranes.
