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This book presents a rigorous and comprehensive treatment of the mathematical theory and real-world applications of porous systems, with a special focus on their asymptotic behavior. It combines analytical, numerical, and computational perspectives to bridge fundamental science and engineering applications, making it relevant to mathematicians, physicists, engineers, and material scientists. It also synthesizes the mathematical foundations, modeling strategies, and engineering practices of porous media systems with asymptotic behavior as a unifying theme, which empowers the readers to model, analyze, and design next-generation porous systems across diverse disciplines.