Our book presents a new account of the field of Analytical Mechanics, often interchangeably referred to as Theoretical Mechanics, Classical Mechanics or Classical Dynamics. It is, by far, the oldest branch of the venerable edifice of Theoretical Physics. The development of analytical mechanics is closely connected with the works of many of the most famous historical figures of physics including those of Isaac Newton (1642-1727), Leonhard Euler (1707-1783), Joseph-Louis Lagrange (1736-1813), Carl Jacobi (1804-1851) and William Hamilton (1805-1865). Analytical mechanics lies at the heart of all branches of theoretical physics. It provides the fundamental concepts and methods other branches are based on. Despite its long history, analytical mechanics continues to be topic of active research with key novel insights achieved only during the last few decades, most notably in the context of non-linear dynamics and chaos and the classical-quantum correspondence in complex systems.Our book attempts to provide a fresh look at this venerable subject that should help to prepare students for their further study by emphasizing the close connections between analytical mechanics and many current topics of a modern physics curriculum.