This textbook presents an extensive exploration of modern and classical optimization methods designed for students, educators, and practitioners across engineering, computer science, economics, and applied mathematics. The text is organized to build foundational understanding before progressing to advanced concepts, ensuring a clear and structured learning pathway.The book begins with a structured introduction to optimization, covering fundamental concepts, historical background, and problem formulation, followed by a MATLAB section that builds essential skills in scripting, visualization, and documentation. It presents key mathematical preliminaries—linear algebra, calculus, Taylor series, and optimization basics—before moving into analytical and numerical solutions of algebraic equations. Major optimization areas are explored in detail, including unconstrained optimization, linear and quadratic programming with classical methods and MATLAB implementations, nonlinear programming with feasible regions and graphical techniques, and mixed¿integer programming using enumeration and branch¿and¿bound approaches. The text further covers multi¿objective optimization through Pareto optimality and conversion techniques, dynamic programming and shortest¿path algorithms for sequential decision processes, and concludes with intelligent optimization methods such as genetic algorithms, particle swarm optimization, and MATLAB’s Global Optimization Toolbox, offering a comprehensive blend of theoretical foundations and practical computational applications.Each chapter balances theoretical exposition, mathematical formulation, manual problem¿solving methods, and detailed computational examples. By bridging theory with hands¿on practice, this textbook serves as a comprehensive and versatile resource, making it indispensable for learners and professionals seeking strong grounding and practical fluency in optimization.