  This paper addresses the three following questions. (i) How the structures of
group and of chain of groups enter nuclear, atomic and molecular spectroscopy?
(ii) How these structures can be exploited, in a quantum- mechanical framework,
in the problems of state labelling and (external) symmetry breaking? (iii) How
it is possible to associate a Wigner-Racah algebra to a group or a chain of
groups for making easier the calculation of quantum-mechanical matrix elements?
Numerous examples illustrate the philosophy of qualitative and quantitative
applications to spectroscopy.
