This book offers a comprehensive, mathematically grounded introduction to multi-attribute decision-making (MADM) for undergraduate, graduate, and doctoral students, as well as researchers in engineering, management, economics, and biology. It bridges theory and practice, covering fundamental concepts, advanced methods, and MATLAB implementations. Topics include critical, subjective, objective, and comprehensive weighting methods, ranking techniques, and their integration for solving complex decision problems. The book addresses challenges such as ranking abnormalities, complexity, and applicability in emerging applications. It also explores fuzzy MADM for handling uncertainty and non-sharp boundaries, highlighting recent research directions and open challenges. Filling a gap in the literature, this book serves as a valuable resource for academics and professionals seeking to apply MADM in dynamic, interdisciplinary contexts.