This monograph is concerned with Galois theoretical embedding problems of socalled Brauer type with a focus on 2groups and on finding explicit criteria for solvability and explicit constructions of the solutions. The advantage of considering Brauer type embedding problems is their comparatively simple condition for solvability in the form of an obstruction in the Brauer group of the ground field. The book presupposes knowledge of classical Galois theory and the attendant algebra. Before considering questions of reducing the embedding problems and reformulating the solvability criteria, the author provides the necessary theory of Brauer groups, group cohomology and quadratic forms. The book will be suitable for students seeking an introduction to embedding problems and inverse Galois theory. It will also be a useful reference for researchers in the field. Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in embedding problems and inverse Galois theory. Reviews "But if you wish to learn about Brauer type embedding problems, and if you want to see a crystalclear and beautiful picture with a number of delightful examples, with a friendly and witty guide, you cannot do better than to read this fine book by Arne Ledet."  CMS Notes "Throughout the monograph, presentations are very crisp and clear. Each chapter is supplemented by a large collection of exercises. The monograph may be used as a textbook for an advanced algebra course."  Zentralblatt Math Table of Contents  Galois theory
 Inverse Galois theory and embedding problems
 Brauer groups
 Group cohomology
 Quadratic forms
 Decomposing the obstruction
 Quadratic forms and embedding problems
 Reducing the embedding problem
 Profinite Galois theory
 Bibliography
 Index
