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This book offers a clear and structured introduction to the calculus of variations, a subject that lies at the heart of modern mathematics and theoretical physics. Designed to balance rigor with accessibility, the text guides readers from foundational concepts to more advanced applications, making it suitable for senior undergraduate and postgraduate students as well as instructors and researchers seeking a reliable reference. Beginning with the basic principles and techniques, the book gradually develops the elementary theory of variational methods, emphasizing necessary conditions for extrema and their practical significance. Core topics include Euler–Lagrange equations, canonical equations, conservation laws, and variational principles of mechanics, presented with strong intuitive and physical motivation. Subsequent chapters extend the discussion to field theory, sufficient conditions for weak and strong extrema, and systems with infinitely many degrees of freedom. The final sections introduce direct methods in the calculus of variations, providing readers with a glimpse of modern approaches to the subject. Each chapter is complemented by carefully designed problems that reinforce theoretical understanding and encourage independent thinking. A selected bibliography supports further exploration of the literature. With its logical organization, modern perspective, and emphasis on applications, this book serves as an effective learning tool and a valuable addition to the mathematical sciences library.