The book is a textbook on arithmetic geometry. The exposition is built around the concept of an unbranched Brauer group of an algebraic variety. Topics covered in the book include Galois cohomology, Brauer groups, obstacles to stable rationality, arithmetic and quadric geometry, Weyl scalar restriction, algebraic tori, an example of an irrational stable rational variety, Brauer-Manin obstacles. All material is divided into relatively simple tasks, provided with detailed instructions.