  We measure the shear viscosity in a two-component Fermi gas of atoms, tuned
to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms
strongly interact and exhibit universal behavior, where the equilibrium
thermodynamic properties and the transport coefficients are universal functions
of the density $n$ and temperature $T$. We present a new calibration of the
temperature as a function of global energy, which is directly measured from the
cloud profiles. Using the calibration, the trap-averaged shear viscosity in
units of $\hbar\,n$ is determined as a function of the reduced temperature at
the trap center, from nearly the ground state to the unitary two-body regime.
Low temperature data is obtained from the damping rate of the radial breathing
mode, while high temperature data is obtained from hydrodynamic expansion
measurements. We also show that the best fit to the high temperature expansion
data is obtained for a vanishing bulk viscosity. The measured trap-averaged
entropy per particle and shear viscosity are used to estimate the ratio of the
shear viscosity to the entropy density, which is compared that conjectured for
a perfect fluid.
