A review is given of the theory of magnetic groups and of their unitary corepresentations. Particular application is made to magnetic space groups, this part of the work being set in the framework of little-group theory. The symmetry problems in physics which lead to magnetic groups are analyzed and various applications of the theory to such problems are pointed out. Finally a method is given for obtaining the Kronecker products of corepresentations of magnetic groups, and an example is presented in which the unitary subgroup of the magnetic group is the point group ${\mathrm{C}}_{2v}$.

DOI:https://doi.org/10.1103/RevModPhys.40.359