This monograph studies decompositions of the Jacobian of a smooth
projective curve, induced by the action of a finite group, into a
product of abelian subvarieties. The authors give a general theorem on
how to decompose the Jacobian which works in many cases and apply it for
several groups, as for groups of small order and some series of groups.
In many cases, these components are given by Prym varieties of pairs of
subcovers. As a consequence, new proofs are obtained for the classical
bigonal and trigonal constructions which have the advantage to
generalize to more general situations. Several isogenies between Prym
varieties also result.