  Roughly speaking a solitary wave is a solution of a field equation whose
energy travels as a localized packet and which preserves this localization in
time. A soliton is a solitary wave which exhibits some strong form of stability
so that it has a particle-like behavior. In this paper, we prove a general,
abstract theorem (Theorem 26) which allows to prove the ex istence of a class
of solitons. Such solitons are suitable minimizers of a constrained functional
and they are called hylomorphic solitons. Then we apply the abstract theory to
problems related to the nonlinear Schr\"odinger equation (NSE) and to the
nonlinear Klein-Gordon equation (NKG).
