The Brauer–Grothendieck Group

“The book gives a comprehensive, clear, up-to date presentation of the theory, including most proofs. A particular strength is that it nicely collects many results, examples and counterexamples from various areas of algebraic and arithmetic geometry … . the book fills a wide gap and is a most welcome addition to the literature.” (Stefan Schröer, zbMATH 1490.14001, 2022)

“This book has collected in one place much of the fundamental cohomological theory of the Brauer group, along with excellent references. It then gives some coverage of further results, especially on the two important topics of obstructions to rationality and obstructions to the Hasse principle. For whatever is not included in this book, it gives a thorough and coherent overview of the relevant literature. Approximately four hundred references are given.” (Thomas Benedict Williams, Mathematical Reviews, September, 2022)