A review has been made of the spin Hamiltonian forms for all the 32 po
int groups, including linear magnetic field-dependent terms in spin op
erators All spin operators (O) over cap(1)(m), (O) over cap(3)(m), (O)
over cap(5)(m), <(Omega)over cap>(m)(1), <(Omega)over cap>(m)(3), and
<(Omega)over cap>(m)(5). All spin operators, as well as their matrix
elements, to be used in constructing spin Hamiltonian matrices, have b
een listed. The various point group aggregates for distinct spin-Hamil
tonian forms have been classified. In addition, descent of symmetry po
int groups, useful for studying structural phase transitions, have bee
n indicated.