Multiscale and Adaptivity: Modeling Numerics and Applications : C.I.M.E. Summer School Cetraro Italy 2009<P>Editors: Giovanni Naldi Giovanni Russo< P> This book is a collection of lecture notes for the CIME course on Multiscale and Adaptivity: Modeling Numerics and Applications held in Cetraro (Italy) in July 2009. Complex systems arise in several physical chemical and biological processes in which length and time scales may span several orders of magnitude. Traditionally scientists have focused on methods that are particularly applicable in only one regime and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power the complexity of such systems precludes their being treated directly with traditional tools and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers coming from different areas of Applied Mathematics have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses. AdaptiveWavelet Methods Heterogeneous Mathematical Models in Fluid Dynamics and Associated Solution Algorithms Primer of Adaptive Finite Element Methods Mathematically Founded Design of Adaptive Finite Element Software.