Cohomology of Number Fields

• Part I Algebraic Theory: Cohomology of Profinite Groups.- Some Homological Algebra.- Duality Properties of Profinite Groups.- Free Products of Profinite Groups.- Iwasawa Modules.- Part II Arithmetic Theory: Galois Cohomology.- Cohomology of Local Fields.- Cohomology of Global Fields.- The Absolute Galois Group of a Global Field.- Restricted Ramification.- Iwasawa Theory of Number Fields.- Anabelian Geometry.- Literature.- Index.

From the reviews of the second edition: "The publication of a second edition gives me a chance to ... emphasize what an important book it is. ... the book a necessary part of the number theorist's library. That it's also well written, clear, and systematic is a very welcome bonus. ... There are many goodies here ... . it is an indispensable book for anyone working in number theory. ... Neukirch, Schmidt, and Wingberg have, in fact, produced ... authoritative, complete, careful, and sure to be a reliable reference for many years." (Fernando Q. Gouvea, MathDL, May, 2008) "The second edition will continue to serve as a very helpful and up-to-date reference in cohomology of profinite groups and algebraic number theory, and all the additions are interesting and useful. ... the book is fine as it is: systematic, very comprehensive, and well-organised. This second edition will be a standard reference from the outset, continuing the success of the first one." (Cornelius Greither, Zentralblatt MATH, Vol. 1136 (14), 2008)