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The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramificatio

Algebraic fields. --- Galois theory. --- Homology theory. --- Cohomology theory --- Contrahomology theory --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Number Theory. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Geometry, algebraic. --- Mathematics. --- Algebraic geometry. --- Group theory. --- Number theory. --- Algebraic fields --- Galois theory --- Homology theory --- 511.6 --- Algebraic topology --- Equations, Theory of --- Group theory --- Number theory --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- 511.6 Algebraic number fields --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of