Damping causes energy dissipation in buildings while they are under earthquake or wind excitations and resulting decrement in structural responses. There are several approaches to increase the building’s damping among them using Tuned Mass Damper (TMD). TMD is a device consisting of a (or a few) mass(s), spring(s), and damper(s) that is attached to a structure in the specific points in order to reduce the dynamic response of the structure. The purpose of using TMD is to produce an artificial force originated from the mass of TMD in order to counteract the structural vibration at which the TMD is installed. TMD is most effective for periodic excitations and wind loads. In this book, the dynamic formulations and applications of TMD in structures are investigated.