This book reports recent mathematical developments in the DFG Priority Programme ''Analysis, Modeling and Simulation of Multiscale Problems'', which started as a German research initiative in 2006. The field of multiscale problems occurs in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. Recently developed tools are described in a comprehensive manner. This book provides the state of the art on the mathematical foundations of the modeling and the efficient numerical treatment of such problems.

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