The book collects a selection of papers most of which are revised and enriched versions of the contributions presented at the 12th Symposium on Trends of Applications of Mathematics to Mechanics (STAMM) which was sponsored by the International Society for the Interaction between Mathematics and Mechanics (ISIMM) and held in Maiori (Salerno), Italy from September 29th to October 4th, 2002. The Symposium attracted many 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 have long been recognized and each of them get benefits and stimuli by open problems, methods and results emerging from the other one. The book collects 22 papers which contribute special investigations and more wide presentations of linear and nonlinear problems. It is with the deepest gratitude to the authors that have contributed to the volume and to the publisher, for his highly professional assistance, that the editors submit this book to the international mathematics and mechanics communities.