An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self contained setting Lagrangian and Hamiltonian dynamics is the continuation of Newton s classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics Lagrangian and Hamiltonian dynamics also acts as a gateway toabstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers Journeying in a self contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter disciplinary applications The book contains some unusual topics for a classical mechanics textbook Most notable examples include the classical wavefunction , Koopman von Neumann theory, classical density functional theories, the vakonomic variational principle for non holonomic constraints, the Gibbs Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometryPeter Mann completed his undergraduate degree in Chemistry at the University of St Andrews He is now a PhD student at the University of St Andrews investigating spreading phenomena on complex networks and how antibiotic resistance proliferates on different network topologies