  This is a textbook on arithmetic geometry with special regard to unramified
Brauer groups of algebraic varieties. The topics include Galois cohomology,
Brauer groups, obstructions to stable rationality, arithmetic and geometry of
quadrics, Weil restriction of scalars, algebraic tori, an example of a stably
rational non-rational variety, Brauer-Manin obstruction. All material is split
into locally trivial problems with detailed hints.
