This book presents in a systematic form a solid theoretical background for transport of non-symmetric beams in rotating ion-optical systems. The theoretical considerations are applied to the transport of ion-therapy beams in rotating ion gantries. Different techniques for matching the rotating gantries to the fixed beam transfer-lines are described, analysed and critically reviewed. Their working principles are explained and their application potential is discussed. Examples of ion-optical systems representing different matching strategies are presented and their ion-optical properties are analysed. Transport of non-symmetric beams in these ion-optical systems is demonstrated by computer simulations.