This dissertation describes the first experimental measurement of the energy and interaction dependent shear viscosity $eta$ and bulk viscosity $zeta$ in the hydrodynamic expansion of a two-component Fermi gas near a broad collisional (Feshbach) resonance. This expansion also provides a precise test of scale invariance and an examination of local thermal equilibrium as a function of interaction strength. After release from an anisotropic optical trap, we observe that a resonantly interacting gas obeys scale-invariant hydrodynamics, where the mean square cloud size $langle{mathbf{r}}^2angle=langle x^2+y^2+z^2angle$ expands ballistically (like a noninteracting gas) and the energy-averaged bulk viscosity is consistent with zero, $0.00(0.04),hbar,n$, with $n$ the density. In contrast, the aspect ratios of the cloud exhibit anisotropic ``elliptic;; flow with an energy-dependent shear viscosity. Tuning away from resonance, we observe conformal symmetry breaking, where $langle{mathbf{r}}^2angle$ deviates from ballistic flow. We find that $eta$ has both a quadratic and a linear dependence on the interaction strength $1/({k_{FI}a})$, where $a$ is the s-wave scattering length and $k_{FI}$ is the Fermi wave vector for an ideal gas at the trap center. At low energy, the minimum is less than the resonant value and is significantly shifted toward the BEC side of resonance, to $1/(k_{FI}a) = 0.2$.
