Engineers are becoming increasingly aware of the problems caused by vibration in engineering design. Vibration control is a key factor in preventing detrimental results from vibration.Smart structures with embedded PZT patches have received attention in vibration control of structure. Adaptive vibration control and sliding mode control are active vibration controls that use intelligent actuators, sensors with adaptive and sliding mode control to reduce vibrations. The adaptive vibration control schemes such as adaptive feedforward LMS and model reference adaptive control are derived and demonstrated with application examples. Moreover, the adaptive control schemes with sliding mode compensator are investigated. This book is an essential reading for engineers and scientists working in the fields of intelligent materials, structural vibration, advanced control and related smart technologies. It is an introduction to the adaptive vibration control schemes of flexible structures. It will also be of interest to senior undergraduate and graduate students as well as aerospace, mechanical, electrical design engineers who want to acquire some background in vibration control.