  We observe multi-step condensation of sodium atoms with spin $F=1$, where the
different Zeeman components $m_F=0,\pm 1$ condense sequentially as the
temperature decreases. The precise sequence changes drastically depending on
the magnetization $m_z$ and on the quadratic Zeeman energy $q$ (QZE) in an
applied magnetic field. For large QZE, the overall structure of the phase
diagram is the same as for an ideal spin 1 gas, although the precise locations
of the phase boundaries are significantly shifted by interactions. For small
QZE, antiferromagnetic interactions qualitatively change the phase diagram with
respect to the ideal case, leading for instance to condensation in $m_F=\pm 1$,
a phenomenon that cannot occur for an ideal gas with $q>0$.
