Focuses on canonical-form characterizations of isometries on Banach spaces. This monograph explores the topic in the context of vector-valued function spaces and operator spaces. It looks at some of the wide variety of methods used in addressing the characterization problem in various types of spaces. "This is a well-written, highly self-contained book which presents the results and their proofs in an accessible way. The results are complemented with an interesting Notes and Remarks section at the end of each chapter which points the interested reader to paths for further investigation. An extensive bibliography is provided. The two volumes provide not only a very good introduction to the subject but also a nice reference tool for experts."-Miguel Martin, Mathematical Reviews, Issue 2009i Praise for Volume One:"This is a very well-written book. ? The authors have done a remarkable job in collecting this material and in exposing it in a very clear style. It will be an important reference tool for analysts, experts, and nonexperts, and it will provide a clear and direct path to several topics of current research interest."-Juan J. Font, Mathematical Reviews, Issue 2004j