  In contrast to WIMPs, light Dark Matter candidates have increasingly come
under the focus of scientific interest. In particular the QCD axion is also
able to solve other fundamental problems such as CP-conservation in strong
interactions. Galactic axions, axion-like particles and hidden photons can be
converted to photons at boundaries between materials of different dielectric
constants under a strong magnetic field. Combining many such surfaces, one can
enhance this conversion significantly using constructive interference and
resonances. The proposed MADMAX setup containing 80 high dielectric disks in a
\SI{10}{\tesla} magnetic field would probe the well-motivated mass range of
$40$--\SI{400}{\micro\electronvolt}, a range which is at present inaccessible
by existing cavity searches. We present the foundations of this approach and
its expected sensitivity.
