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The structure theory of abelian extensions of commutative§rings is a subjectwhere commutative algebra and algebraic§number theory overlap. This exposition is aimed at readers§with some background in either of these two fields. Emphasis§is given to the notion of a normal basis, which allows one§to view in a well-known conjecture in number theory§(Leopoldt's conjecture) from a new angle. Methods to§construct certain extensions quite explicitly are also§described at length.