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Until rather recently, number theory, or arithmetic as some prefer to call it, has been conspicuous for the quality rather than for the number of its own devotees. At the same time it is perhaps unique in the enthusiasm eloquently expressed in many utterances of such men as Euler, Eisenstein, Hilbert... The method to be followed here is historical throughout. No specific knowledge is expected of the reader, and it is the author's fond hope that some readers at least will find it possible to get theory initiation into number theory by following the itinerary retraced in this volume