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The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena are a challenging topic of very active research. This volume collects lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
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Table of Contents

Problems with multiple scales.- From discrete systems to continuous variational problems: an introduction.- Relaxation for bulk and interfacial energies.- Convergence of Dirichlet forms on fractals.- Homogenization in perforated domains.- Homogenization of random non stationary parabolic operators.- Problems with concentration.- ?-convergence for concentration problems.- Gamma-convergence of gradient flows and applications to Ginzburg-Landau vortex dynamics.- PDE analysis of concentrating energies for the Ginzburg-Landau equation.

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