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Optimization lies at the core of modern science, engineering, and decision-making, providing systematic methods to identify the best possible solutions under given constraints. This book presents a comprehensive and integrated treatment of optimization, beginning with foundational concepts and mathematical prerequisites and progressing through linear, nonlinear, combinatorial, dynamic, stochastic, and convex optimization frameworks. Emphasis is placed on both theoretical understanding and algorithmic implementation, ensuring that readers not only grasp underlying principles but also learn how to apply them to real-world problems. Historical developments are interwoven with contemporary methods to highlight the evolution of optimization as a discipline. Each chapter is structured to balance rigor with intuition, supported by classical examples, algorithms, and practical applications across engineering, economics, artificial intelligence, and the natural sciences. Designed for students, researchers, and practitioners, this book aims to build strong conceptual foundations while also introducing advanced topics and emerging frontiers. Ultimately, it seeks to cultivate analytical thinking and equip readers with versatile optimization tools for solving complex, real-world challenges.