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. Gouv a, 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).