  Extending over three Hubble Space Telescope (HST) cycles, the Hubble Frontier
Fields (HFF) initiative constitutes the largest commitment ever of HST time to
the exploration of the distant Universe via gravitational lensing by massive
galaxy clusters. We here present models of the mass distribution in the six HFF
cluster lenses, derived from a joint strong- and weak-lensing analysis anchored
by a total of 88 multiple-image systems identified in existing HST data. The
resulting maps of the projected mass distribution and of the gravitational
magnification effectively calibrate the HFF clusters as gravitational
telescopes. Allowing the computation of search areas in the source plane, these
maps are provided to the community to facilitate the exploitation of
forthcoming HFF data for quantitative studies of the gravitationally lensed
population of background galaxies. Our models of the gravitational
magnification afforded by the HFF clusters allow us to quantify the
lensing-induced boost in sensitivity over blank-field observations and predict
that galaxies at $z>10$ and as faint as m(AB)=32 will be detectable, up to 2
magnitudes fainter than the limit of the Hubble Ultra Deep Field.
