The paper introduces minimal models for altermagnetism, a novel form of magnetic order characterized by vanishing net magnetization but time-reversal symmetry breaking and momentum-dependent spin-split band structures. The authors construct tight-binding models for non-symmorphic space groups with a sublattice defined by two magnetic atoms, applicable to various crystal structures including monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic materials. These models can describe $d$-wave, $g$-wave, and $i$-wave altermagnetism. By examining the altermagnetic susceptibility and mean-field instabilities within a Hubbard model, they reveal that these models yield altermagnetic ground states and a Berry curvature linear in the spin-orbit coupling. The models are applied to materials such as RuO$_2$, MnF$_2$, FeSb$_2$, $\kappa$-Cl, CrSb, and MnTe, demonstrating their versatility and accuracy in capturing key properties of these materials. The paper also discusses the stabilization of altermagnetism through band degeneracies and the role of SOC in generating a linear Berry curvature, which leads to a large crystal Hall effect.The paper introduces minimal models for altermagnetism, a novel form of magnetic order characterized by vanishing net magnetization but time-reversal symmetry breaking and momentum-dependent spin-split band structures. The authors construct tight-binding models for non-symmorphic space groups with a sublattice defined by two magnetic atoms, applicable to various crystal structures including monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic materials. These models can describe $d$-wave, $g$-wave, and $i$-wave altermagnetism. By examining the altermagnetic susceptibility and mean-field instabilities within a Hubbard model, they reveal that these models yield altermagnetic ground states and a Berry curvature linear in the spin-orbit coupling. The models are applied to materials such as RuO$_2$, MnF$_2$, FeSb$_2$, $\kappa$-Cl, CrSb, and MnTe, demonstrating their versatility and accuracy in capturing key properties of these materials. The paper also discusses the stabilization of altermagnetism through band degeneracies and the role of SOC in generating a linear Berry curvature, which leads to a large crystal Hall effect.