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Mathematics is a universal language. Differential equations, mathematical modeling, numerical methods and computation form the deep infrastructure of engineering and sciences. In this context mathematical modeling is a very powerful tool for studying engineering, natural systems and human society. This interdisciplinary book contains a comprehensive overview of the progress achieved up to date in the modelling of coupled phenomena, computational mathematics and mechanics, heat transfer, fluid-structure interactions, biomechanics, flow of mass and energy in porous media. These are all among the different topics covered in this book through completely solved practical problems. Numerical subjects such as grid generation, optimization, finite elements, finite differences, spectral methods, boundary elements, finite volumes and meshless methods are also discussed in detail using real examples. The book provides a thorough presentation of the existing worldwide numerical techniques, but applied to concrete, useful topics. The models and solutions here presented describe various systems, mechanical, biological, geophysical, technical, ecological, etc. The book is organized in thirty six chapters written by distinguished experts in each one of the different fields covered in its pages. The aim is to present the current state of knowledge in numerical engineering practice, recent and ongoing developments with the projection of new ideas for future research on applied computational engineering mathematics. The audience of this book are people working on any branch of engineering: structural, civil, mechanics, geology, geophysics, aquifers, petroleum reservoirs, applied mathematicians, physicists, other scientists and students of any of these areas. They will find in this book the most recent advances in the different engineering topics covered.