<p>Spin-imbalanced Fermi gases serve as a testbed for fundamental notions and are efficient table-top emulators of a variety of quantum matter ranging from neutron stars, the quark-gluon plasma, to high critical temperature superconductors. A macroscopic quantum phenomenon which occurs in spin-imbalanced Fermi gases is that of phase separation; in three dimensions, a spin-balanced, fully-paired superfluid core is surrounded by an imbalanced normal-fluid shell, followed by a fully polarized shell. In one-dimension, the behavior is reversed; a balanced phase appears outside a spin-imbalanced core. This thesis details the first density profile measurements and studies on spin-imbalanced quasi-2D Fermi gases, accomplished with high-resolution, rapid sequential spin-imaging. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a 2D system. Data for normal-fluid mixtures are well fit by a simple 2D polaron model of the free energy. Not predicted by the model is an observed phase transition to a spin-balanced central core above a critical polarization.</p> / Dissertation