Cohomology of Profinite Groups
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The basis of class field theory and Galois cohomology, which are used for deriving almost all the results on p-extensions in this book, is the calculus of cohomology groups of discrete modules of profinite groups. It is this calculus that we have to build first. Here we mainly have to take the requirements for Galois cohomology into consideration, whereas the cohomology of finite groups that is needed for class field theory is only developed as far as is necessary for the formulation of the theorems that will be important for us. See also J.P. Serre [51, Chap. VI–XI].
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