The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. New efficient, publicly available or even commercial tools are proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened. They are concerned not only with applications of well known enclosure methods or the development of new-self validating algorithms, but also transfer the mechanisms and design process known from these areas to other fields. The 31 contributions to this proceedings volume were carefully selected from a much larger number of submissions.