An Introduction to Galois Cohomology and its Applications

This book begins with a concrete motivational example, and proceeds to develop the cohomology theory to explain the example. The development itself is fine, but suffers from a few defects. The line between the abelian and nonabelian case is not always explicit enough for people learning the subject, in my view. For example, the definition of higher cohomology is preceded by one sentence at the bottom of the previous page explaining that the algebraic group in question is abelian. The section concludes with the statement that from now on when higher cohomology is discussed, the assumption is, "the set A has appropriate structure." This is confusing to a person reading about this subject for the first time. When can we discuss higher Galois cohomology? Complicating matters, the next section contains several results where the assumptions necessary for the propositions to even make sense are not clearly spelled out. Using this book as a reference for learning the subject is a bad idea mainly because of this defect. The exposition itself if fine. The proofs are clear and well-written.