  The review considers the peculiarities of symmetry breaking and symmetry
transformations and the related physical effects in finite quantum systems.
Some types of symmetry in finite systems can be broken only asymptotically.
However, with a sufficiently large number of particles, crossover transitions
become sharp, so that symmetry breaking happens similarly to that in
macroscopic systems. This concerns, in particular, global gauge symmetry
breaking, related to Bose-Einstein condensation and superconductivity, or
isotropy breaking, related to the generation of quantum vortices, and the
stratification in multicomponent mixtures. A special type of symmetry
transformation, characteristic only for finite systems, is the change of shape
symmetry. These phenomena are illustrated by the examples of several typical
mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and
metallic grains. The specific features of the review are: (i) the emphasis on
the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii)
the analysis of common properties of physically different finite quantum
systems; (iii) the manifestations of symmetry breaking in the spectra of
collective excitations in finite quantum systems. The analysis of these
features allows for the better understanding of the intimate relation between
the type of symmetry and other physical properties of quantum systems. This
also makes it possible to predict new effects by employing the analogies
between finite quantum systems of different physical nature.
