This text provides a rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented should permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. Civil, mechanical or aeronautical engineers should find in the book a mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems.