  We study the Fermi liquid properties of the cold atomic dipolar Fermi gases
with the explicit dipolar anisotropy using perturbative approaches. Due to the
explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the
$d_{r^2-3z^2}$-type in three dimensions and of the $d_{x^2-y^2}$-type in two
dimensions. The fermion self-energy, effective mass, and Fermi velocity develop
the same anisotropy at the Hartree-Fock level proportional to the interaction
strength. The Landau interaction parameters in the isotropic Fermi liquids
become the tri-diagonal Landau interaction matrices in the dipolar Fermi
liquids which renormalize thermodynamic susceptibilities. With large dipolar
interaction strength, the Fermi surface collapses along directions
perpendicular to the dipole orientation. The dynamic collective zero sound
modes exhibit an anisotropic dispersion with the largest sound velocity
propagating along the polar directions. Similarly, the longitudinal p-wave
channel spin mode becomes a propagating mode with an anisotropic dispersion in
multi-component dipolar systems.
