Since Lord Rayleigh introduced the idea of viscous damping in his classic work "The theory of sound" (1877) it has become standard practice to use this approach in dynamics covering a huge range of applications from aerospace to civil engineering. However, in majority of practical cases this approach is adopted more for mathematical convenience than modelling the physics of vibration damping. Over the past decade extensive research have been done on more general 'non-viscous' damping models and vibration of non-viscously damped systems. This book is the first comprehensive text to cover vibration problems with general non-viscous damping. The author will draw on his considerable research experience to produce a volume covering: non-viscously damped single and multi-degree of freedom systems; continuous systems with non-local and non-viscous damping; identification of non-viscous damping; computational aspects of non-proportional and non-viscous damping and sensitivity analysis. The text will be written from a vibration theory standpoint, with numerous worked examples relevant across a wide range of mechanical, aerospace and structural engineering applications.