From the reviews: "The broad lines of Kummer's number-theoretic ideas now form an essential part of our heritage: it is fascinating to follow the details of their evolution. Volume I consists of Kummer's number theory. It constitutes a unity of thought and spirit almost from first sentence to last. One of the joys of reading it is in the double spectacle: the steady train of mathematical content, unimpeded by lack of basic algebraic number theory; while here and there, to serve problems at hand, the deft, unobtrusive forging of pieces of present-day technique. It is not hard to get into, even for those of us who have had little contact with the history of our subject. Cleft though one may think one is from historical sources, on reading Kummer one finds that the rift is jumpable, the jump pleasurable. The reader is greatly helped in this jump in two ways. Firstly, includ.".