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This book provides an in-depth, comprehensive, and comprehensible description of the theoretical background and numerical methodologies corresponding to advanced particle methods formulated in classical Newtonian mechanics for simulation of fluids, structures, and their interactions. Particle methods are regarded as new-generation computational technology with a broad range of applications in engineering and science. Advanced particle methods refer to the latest developed particle methods with high stability, accuracy, conservation, and convergence properties. Distinctively, the described advanced particle methods are characterized by a clear, consistent mathematical–physical background, the absence of artificial numerical stabilizers that often require parameter tuning, rigorous satisfaction of boundary conditions, and excellent numerical results that have been extensively and scrupulously verified with respect to reliable analytical and experimental reference solutions