Dynamical symmetries in the structure of nuclei

The use of spectrum generating algebras in the description of the Anuclear many-body system is reviewed. General notions of symmetry and dynamical symmetry in Aquantum mechanics are introduced with the help of simple examples. It is then indicated Ahow techniques based on symmetry considerations can be used to find the analytical Asolutions for the problem of an aggregate of interacting particles (bosons and/or fermions). Some Aolder ideas due to Wigner, Racah and Elliott are succinctly summarized to put more recent Aadvances in a proper perspective. It is then shown that similar techniques are used in a Amodel of the nucleus in terms of interacting bosons due to Arima and Iachello. Subsequent Aextensions of this model to odd-mass nuclei lead to the consideration of mixed systems of Abosons and fermions and, most notably, to supersymmetry.