Giant resonances are collective excitations of the atomic nucleus, a typical quantum many-body system. The study of these fundamental modes has in many respects contributed to our understanding of the bulk behaviour of the nucleus and of the dynamics of non-equilibrium excitations. Although the phenomenon of giant resonances has been known for more than 50 years, a large amount of information has only been obtained in the last ten years. This book gives a comprehensive and up-to-date account of our present knowledge of giant resonances. It presents the experimental facts and the techniques used to obtain that information, describes how these facts fit into theoretical concepts and how this allows us to determine various nuclear properties which are otherwise difficult to obtain. Included as an introduction is an overview of the main facts, a short history of how the field has developed, and a discussion of the prospects for the future.