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.
