Boundary representations are an important tool for studying subalgebras of C*-algebras. Boundary representations were defined almost fifty years ago, but it wasn't until extremely recently that they were proven to exist in all cases, and there are no general methods of computing them. In my thesis I compute the boundary representations for an algebra of holomorphic cross-sections of a flat holomorphic matrix bundle. I further show this subalgebra shares structural properties with its C*-envelope.