This book is a research monograph that addresses the basic issues in controlling large, flexible space structures (LFSS), and presents some controller synthesis methods developed by the author. The main problem considered is that of controller synthesis for precision attitude control and vibration suppression in LFSS. The bulk of the book presents two basic approaches for controller synthesis: 1. a class of "dissipative" controllers which utilize collocated actuators and sensors, and 2. a class of model-based compensators. The book will serve to stimulate research activity in control theory with application to LFSS, and will be very useful to researchers, practising engineers, academic faculty, and students in control and aerospace sciences. The background required of the reader is familiarity with basic control theory including state variable methods, which is generally attained at the first-year postgraduate level.