This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group and self-consistent mode coupling. Dynamic critical phenomena near a second order phase transition, phase ordering dynamics, dynamics of surface growth and turbulence form the backbone of the book. Applications to a wide variety of systems (e.g. magnets, ordinary fluids, superfluids) are provided covering diverse transport properties (diffusion, sound). It is unique in that it gives a detailed description of perturbation theory for nonlinear continuous systems, it focuses on techniques which can be applied to problems ranging from near equilibrium dynamics to fully developed turbulence, and it provides a discussion of physical properties (e.g. critical ultrasonics) that are generally not covered in text books. Audience: Beginning graduate students, senior undergraduates, researchers.