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This edited book contains a selection of invited and contributed lectures of the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. The book gives an overview of recent developments in numerical analysis, computational mathematics and applications by leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. It will be useful for a wide range of readers giving them a state of the art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.