We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components mF=0,±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization mz 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 mF=±1, a phenomenon that cannot occur for an ideal gas with q\textgreater0.