This thesis presents experiments investigating the
phase diagram of ultracold atomic Fermi gases using radio-frequency
spectroscopy. The tunability of many experimental parameters
including the temperature, the interparticle interaction strength
and the relative population of different Fermions allows to access
very different physical regimes. Radio-frequency spectroscopy has
been developed into an ideal tool to probe correlations between
particles in these different phases. In particular, radio-frequency
spectroscopy of highly population imbalanced atomic Fermi systems
gives access to the impurity problem: A single Fermion, or Boson,
immersed in a sea of Fermions constitutes a polaron, which can be
described by Landau's Fermi liquid theory. A critical interaction
strength can be identified separating the regime of a fermionic
polaron and a bosonic polaron. Radio-frequency spectroscopy of the
polarized superfluid phase allows an accurate measure of the
superfluid gap [Delta] and allows to identify the importance of
Hartree Mean-field energies. Furthermore, it is shown how these
different physical regimes are connected.