  Interacting fermions are ubiquitous in nature and understanding their
thermodynamics is an important problem. We measure the equation of state of a
two-component ultracold Fermi gas for a wide range of interaction strengths at
low temperature. A detailed comparison with theories including Monte-Carlo
calculations and the Lee-Huang-Yang corrections for low-density bosonic and
fermionic superfluids is presented. The low-temperature phase diagram of the
spin imbalanced gas reveals Fermi liquid behavior of the partially polarized
normal phase for all but the weakest interactions. Our results provide a
benchmark for many-body theories and are relevant to other fermionic systems
such as the crust of neutron stars.
