The book is a mostly translated reprint of a report on cohomology of
groups from the 1950s and 1960s, originally written as background for
the Artin-Tate notes on class field theory, following the cohomological
approach. This report was first published (in French) by Benjamin. For
this new English edition, the author added Tate's local duality, written
up from letters which John Tate sent to Lang in 1958 - 1959. Except for
this last item, which requires more substantial background in algebraic
geometry and especially abelian varieties, the rest of the book is
basically elementary, depending only on standard homological algebra at
the level of first year graduate students.