Attenuation of vibration and noise constitutes a growing concern in today's human activities. For more than forty-five years, it was realized that passive attenuation of vibration and noise via dedicated absorbers has limits and the concepts of active vibration and noise control have emerged. Active vibration and noise control are strongly related to control methodology, even if in the past the control community was not the driving force in this field. Almost from the beginning, the uncertainties and changes in the characteristics of the environment (vibrations, noise, system dynamics) have prompted the idea of using an adaptive approach in active vibration or noise control. Addressing some of these issues from a robustness point of view is a much more recent tendency in the field. Practical experience has shown also the limits of using only physical models for designing active vibration or noise control systems, bringing to light the need of dynamic model identification directly from input/output data. The aim of this book is to approach the design of active vibration control systems from the perspective of today's control methodology. In that sense, the first objective is to formulate from the beginning the various design problems encountered in active vibration control as control problems and search for the most appropriate control tools to solve them. Experimental validation of the proposed solutions on relevant test benches is another issue addressed in this book. To make these techniques widely accepted, an appropriate presentation should be given, eliminating theoretical developments unnecessary for the users (which can be found elsewhere) and focusing on algorithms presentation and their use. Nevertheless, the proposed solutions cannot be fully understood and creatively exploited without a clear understanding of the basic concepts and methods and so these are given in-depth coverage.