  This thesis presents experiments probing physics in the crossover between
Bose-Einstein condensation (BEC) and BCS superconductivity using an ultracold
gas of atomic fermions. Scattering resonances in these ultracold gases (known
as Feshbach resonances) provide the unique ability to tune the fermion-fermion
interactions. The work presented here pioneered the use of fermionic Feshbach
resonances as a highly controllable and tunable system ideal for studying the
cusp of the BCS-BEC crossover problem. Here pairs of fermionic atoms have some
properties of diatomic molecules and some properties of Cooper pairs. I present
studies of a normal Fermi gas at a Feshbach resonance and the work required to
cool the gas to temperatures where superfluidity in the crossover is predicted.
These studies culminated in our observation of a phase transition at the cusp
of the BCS-BEC crossover through condensation of fermionic atom pairs. I also
discuss subsequent work that confirmed the crossover nature of the pairs in
these condensates.
