Cohomology of groups

A self-contained presentation of the cohomology theory of discrete modules over profinite groups. Cohomology groups in all positive dimensions and the long cohomology sequence. Cohomology in dimension 0 and -1 for finite groups and the Herbrand quotient. Group extensions. Functorial properties of induced modules and Shapiro's lemma. Behavior of cohomology groups under direct sums and limits. Restriction, inflation and corestriction and their properties. Transfer and the principal ideal theorem. Basics of Galois cohomology (Kummer and Artin-Schreier extensions).