  We study the attractive and repulsive two-component Fermi gas with spin
imbalance in two dimensions. Using a generalized $T$-matrix approximation, we
examine the thermodynamic properties of both attractive and repulsive contact
interacting Fermi gases. The interaction strength, which is characterized by
the bound state energy $E_b=\hbar^2/m a_{2d}^2$ in vacuum, can be adjusted
through a Feshbach resonance. We calculate the interaction energy,
compressibility and spin susceptibility of the two branches of the Fermi gas.
For the repulsive branch, we also find a critical strength of interaction
$a_{2d}^{(c)}$ above which this metastable thermodynamic state becomes
unstable. This critical value depends on the temperature and the spin imbalance
(the "magnetization") of the system.
