  We construct systematic expansions around four and two spatial dimensions for
a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi
gas can be understood as a weakly-interacting system of fermionic and bosonic
degrees of freedom. To the leading and next-to-leading orders in the expansion
over \epsilon=4-d, with d being the dimensionality of space, we determine the
thermodynamic functions, the fermion quasiparticle spectrum, the critical
polarizations, and the critical temperature as functions of the binding energy
of the two-body state. We also show that the unitary Fermi gas near two spatial
dimensions reduces to a weakly-interacting Fermi gas and calculate the
thermodynamic functions and the fermion quasiparticle spectrum in the expansion
over \bar\epsilon=d-2. We discuss the matching of the two systematic expansions
around four and two spatial dimensions in order to extract physical observables
at d=3. We find good agreement of the results with those from recent Monte
Carlo simulations.
