The aim of this volume that presents lectures given at a joint
CIME and Banach Center Summer School, is to offer a broad
presentation of a class of updated methods providing a mathematical
framework for the development of a hierarchy of models of complex
systems in the natural sciences, with a special attention to
biology and medicine. Mastering complexity implies sharing
different tools requiring much higher level of communication
between different mathematical and scientific schools, for solving
classes of problems of the same nature. Today more than ever, one
of the most important challenges derives from the need to bridge
parts of a system evolving at different time and space scales,
especially with respect to computational affordability. As a result
the content has a rather general character; the main role is played
by stochastic processes, positive semigroups, asymptotic analysis,
kinetic theory, continuum theory, and game theory.
General
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