  For a bounded weak Lipschitz domain we show the so called `Maxwell
compactness property', that is, the space of square integrable vector fields
having square integrable weak rotation and divergence and satisfying mixed
tangential and normal boundary conditions is compactly embedded into the space
of square integrable vector fields. We will also prove some canonical
applications, such as Maxwell estimates, Helmholtz decompositions and a static
solution theory. Furthermore, a Fredholm alternative for the underlying
time-harmonic Maxwell problem and all corresponding and related results for
exterior domains formulated in weighted Sobolev spaces are straight forward.
