Collective behavior in systems with many components, blow-ups with emergence of
microstructures are proofs of the double, continuum and atomistic, nature of
macroscopic systems, an issue which has always intrigued scientists and
philosophers. Modern technologies have made the question more actual and
concrete with recent, remarkable progresses also from a mathematical point of
view. The book focuses on the links connecting statistical and continuum
mechanics and, starting from elementary introductions to both theories, it leads
to actual research themes. Mathematical techniques and methods from probability,
calculus of variations and PDE are discussed at length.