  We study the pinning of vortices in thin film superconductors by magnetic
dots in the London approximation. A single dot is in general able to pin
multiple field-induced vortices, up to a saturation number n_s, which can be
much larger than one. However, the magnetic field of the dot also creates
intrinsic vortices and anti-vortices, which must be accounted for. In a
ferromagnetic dot array, the intrinsic anti-vortices are pinned only
interstitially. Much stronger pinning effect is expected of an
antiferromagnetic dot array. Possible realizations of various magnetic
configurations are discussed.
