  The stability of different phases of the three-dimensional non-relativistic
electron gas is analyzed using stochastic methods. With decreasing density, we
observe a {\it continuous} transition from the paramagnetic to the
ferromagnetic fluid, with an intermediate stability range ($25\pm 5 \leq
r_s\leq 35 \pm 5$) for the {\it partially} spin-polarized liquid. The freezing
transition into a ferromagnetic Wigner crystal occurs at $r_s=65 \pm 10$. We
discuss the relative stability of different magnetic structures in the solid
phase, as well as the possibility of disordered phases.
