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Thebookoffersaselectionofpapersmostofwhicharerevisedandenrichedversions of the contributions presented at the 12th Symposium on Trends of Applications of Mathematics to Mechanics (STAMM) which was sponsored by the International - ciety for the Interaction between Mathematics and Mechanics (ISIMM) and held in Maiori (Salerno), Italy, from September 29th to October 4th, 2002. The Symposium attracted leading researchers from around the world who are working at the interface between mathematics and mechanics. The importance of a close link between these two disciplines has long been recognized; each bene?ts from and is stimulated by open problems, methods and results emerging from the other. The book comp- ses 22 papers which report specialized investigations and which contribute broader presentations of linear and nonlinear problems. It is with the deepest gratitude to the authors who have contributed to the volume and to the publisher, for its highly professional assistance, that the editors submit this book to the international mathematics and mechanics communities. The editors gratefully acknowledge the ?nancial support of the following institutions: Gruppo NazionalediFisicaMatematica(GNFM)oftheIstitutoNazionalediAltaMatematica (INDAM), Universita ' degli Studi di Napoli Federico II and Regione Campania.