The present manuscript is an improved edition of a text that first
appeared under the same title in Bonner Mathematische Schriften,
no.26, and originated from a series of lectures given by the author
in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to
provide the reader, acquainted with the basics of algebraic number
theory, a quick and immediate access to class field theory. This
script consists of three parts, the first of which discusses the
cohomology of finite groups. The second part discusses local class
field theory, and the third part concerns the class field theory of
finite algebraic number fields.
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