To devote the first chapter of a book on magicians in the Greek and Roman worlds to a discussion of the concept of magic with which the Greeks operated and which the Romans inherited from them requires explanation and justification. There will be those who feel that such preliminaries can be dispensed with, since they are largely irrelevant to the real business in hand. These are feelings with which I can sympathize, since my own reactions on coming across yet another attempt at defining the notion of magic is dismay combined with a sense of foreboding.