  We study boundary value problems for first-order elliptic differential
operators on manifolds with compact boundary. The adapted boundary operator
need not be selfadjoint and the boundary condition need not be pseudo-local. We
show the equivalence of various characterisations of elliptic boundary
conditions and demonstrate how the boundary conditions traditionally considered
in the literature fit in our framework. The regularity of the solutions up to
the boundary is proven. We show that imposing elliptic boundary conditions
yields a Fredholm operator if the manifold is compact. We provide examples
which are conveniently treated by our methods.
