This book covers the basic principles of nonlinear vibrations which occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques.Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications. This is particularly true in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring.Two broader themes cut across these application areas: (i) vibrationsuppression -- or active damping -- and, (ii) adaptive structures andmachines. The aim of this book is to provide a comprehensive discussionof nonlinear multi-modal structural vibration problems, and then to showhow vibration suppression can be applied to such systems by considering asample set of relevant control techniques. The rationale is to produce avolume which is accessible to practitioners in the application areas, aswell as students and researchers working on related topics. In particular, the aim is to introduce the key concepts of nonlinear vibration to readerswho have an understanding of linear vibration and/or linear control, butno specialist knowledge in nonlinear dynamics or nonlinear control.