The notion of class formation was introduced by Artin-Tate  after earlier work by Weil  and by Hochschild-Nakayama . This notion clarifies the cohomological aspect of class field theory, both in the local and the global cases. The present chapter is restricted to the main properties of class formations; the reader will find in Artin-Tate  further developments (the Šafarevič theorem, Weil groups).
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