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Treats mainly the classical part of the theory of algebraic functions. This book is suitable for graduate students who have some basic knowledge of algebra, topology, and functions of a complex variable.

Teiji Takagi one of the leading number theorists of this century, is most renowned as the founder of class field theory. This volume reflects the stages of his development of this theory. Inspired by a genial idea related to analytic number theory, he developed a beautiful general theory of abelian extensions of algebraic number fields which he addressed at the ICM 1920 at Strasbourg. This report ends with a problem to generalize the results to the case of normal, not necessarily abelian extensions. Up to now this problem has stimulated research. This second edition incorporates the whole...

Iwasawa is one of the most original and influential mathematicians in the 20th century. This Collected Papers of K. Iwasawa contains all 66 published papers, including 11 papers in Japanese, for which English abstracts (by the editors) are attached. Also included is a masterly summery of Iwasawa theory by J. Coates (Cambridge).