In general, electric (charge) radiation or magnetic (current, magnetic moment) radiation can be classified into multipoles E (electric) or M (magnetic) of order 2, e.g., E1 for electric dipole, E2 for quadrupole, or E3 for octupole. In transitions where the change in angular momentum between the initial and final states makes several multipole radiations possible, usually the lowest-order multipoles are overwhelmingly more likely, and dominate the transition.
The emitted particle carries away angular momentum, with quantum number , which for the photon must be at least 1, since it is a vector particle (i.e., it has total angular momentum quantum number| = 1). Thus, there is no radiation from  E0 (electric monopoles) or  M0  (magnetic monopoles, which do not seem to exist).
Since the total angular momentum has to be conserved during the transition, we have that
where  and its z-projection is given by  and where  and  are, respectively, the initial and final angular momenta of the atom. 
The corresponding quantum numbers  and  (-axis angular momentum) must satisfy
and
Parity is also preserved. For electric multipole transitions 
while for magnetic multipoles
Thus, parity does not change for E-even or M-odd multipoles, while it changes for E-odd or M-even multipoles.
These considerations generate different sets of transitions rules depending on the multipole order and type. The expression forbidden transitions is often used, but this does not mean that these transitions cannot occur, only that they are electric-dipole-forbidden. These transitions are perfectly possible; they merely occur at a lower rate. If the rate for an E1 transition is non-zero, the transition is said to be permitted; if it is zero, then M1, E2, etc. transitions can still produce radiation, albeit with much lower transitions rates. The transition rate decreases by a factor of about 1000 from one multipole to the next one, so the lowest multipole transitions are most likely to occur.
Semi-forbidden transitions (resulting in so-called intercombination lines) are electric dipole (E1) transitions for which the selection rule that the spin does not change is violated. This is a result of the failure of LS coupling.