  We consider ${\cal N}=4$ supersymmetric Yang Mills theory on a space with
supersymmetry preserving boundary conditions. The boundaries preserving half of
the 16 supercharges were analyzed and classified in an earlier work by Gaiotto
and Witten. We extend that analysis to the case with fewer supersymmetries,
concentrating mainly on the case preserving one quarter. We develop tools
necessary to explicitly construct boundary conditions which can be viewed as
taking the zero slope limit of a system of D3 branes intersecting and ending on
a collection of NS5 and D5 branes oriented to preserve the appropriate number
of supersymmetries. We analyze how these boundary conditions constrain the bulk
degrees of freedom and enumerate the unconstrained degrees of freedom from the
boundary/defect field theory point of view. The key ingredients used in the
analysis are a generalized version of Nahm's equations and the explicit
boundary/interface conditions for the NS5-like and D5-like impurities and
boundaries, which we construct and describe in detail. Some bulk degrees of
freedom suggested by the naive brane diagram considerations are lifted.
