From the reviews: 'the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book' - M. R. Hestenes in "Journal of Optimization Theory and Applications".'The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems' - L. Schmetterer in "Monatshefte fur Mathematik". 'The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book' - M. Coroi-Nedeleu in "Revue Roumaine de Mathematiques Pures et Appliquees".