The completion of this volume ends a project which has been on our minds for over 20 years. We began the writing of what became the first volume [137] in the fall of 1995. It has been a labor of love and we hope it will prove to be a useful addition to the literature. The original idea was to provide a full survey of the work done in characterizing the form of isometries on various Banach spaces. That turned out to be a task too vast in its extent to be done very successfully, but we have tried to touch on as many of its aspects as possible and to include a large number of references. Isometries are of fundamental importance and interest, and results about them pop up in all kinds of places