  We present detailed measurements of the frequency and damping of three
different collective modes in an ultracold trapped Fermi gas of $^6$Li atoms
with resonantly tuned interactions. The measurements are carried out over a
wide range of temperatures. We focus on the unitarity limit, where the
scattering length is much greater than all other relevant length scales. The
results are compared to theoretical calculations that take into account Pauli
blocking and pair correlations in the normal state above the critical
temperature for superfluidity. We show that these two effects nearly compensate
each other and the behavior of the gas is close to the one of a classical gas.
