Decomposition of Jacobians by Prym Varieties Introduction Preliminaries and basic results Finite covers of curves Covers of degree 2 and 3 Covers of degree 4 Some special groups and complete decomposabality Bibliography Index. 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.