  The pairing of fermions is at the heart of superconductivity and
superfluidity. The recent experimental realization of strongly interacting
atomic Fermi gases has opened a new, controllable way to study novel forms of
pairing and superfluidity. A major controversial issue has been the stability
of superfluidity against an imbalance between the two spin components when the
fermions interact resonantly. Here we present the phase diagram of a
spin-polarized Fermi gas of $^6$Li atoms at unitarity, mapping out the
superfluid phase versus temperature and density imbalance. Using tomographic
techniques, we reveal spatial discontinuities in the spin polarization, the
signature of a first-order superfluid-to-normal phase transition, which
disappears at a tricritical point where the nature of the phase transition
changes from first-order to second-order. At zero temperature, there is a
quantum phase transition from a fully-paired superfluid to a
partially-polarized normal gas. These observations and the implementation of an
in situ ideal gas thermometer provide quantitative tests of theoretical
calculations on the stability of resonant superfluidity.
