  We study the spectral theory for the first-order system $Ju'+qu=wf$ of
differential equations on the real interval $(a,b)$ when $J$ is a constant,
invertible skew-Hermitian matrix and $q$ and $w$ are matrices whose entries are
distributions of order zero with $q$ Hermitian and $w$ non-negative. Also, we
do not pose the definiteness condition customarily required for the
coefficients of the equation. Specifically, we construct minimal and maximal
relations, and study self-adjoint restrictions of the maximal relation. For
these we determine Green's function and prove the existence of a spectral (or
generalized Fourier) transformation. We have a closer look at the special cases
when the endpoints of the interval $(a,b)$ are regular as well as the case of a
$2\times2$ system. Two appendices provide necessary details on distributions of
order zero and the abstract spectral theory for relations.
