Rules that determine which transitions between different energy levels are possible in a system, such as an elementary particle, nucleus, atom, molecule, or crystal, described by quantum mechanics. Transitions cannot take place between any two energy levels. Group theory, associated with the symmetry of the system, determines which transitions, called allowed transitions, can take place and which transitions, called forbidden transitions, cannot take place. Selection rules determined in this way are very useful in analysing the spectra of quantum-mechanical systems.