Lobachevsky's geometry is presented on the basis of school axiomatics of absolute geometry and Lobachevsky's axiom. The first part of the book is devoted to Lobachevsky's planimetry, and the second to stereometry. At the end of each chapter, tasks are given, at the end of the book - answers and instructions to them. This book compares favorably with other manuals on the geometry of Lobachevsky. The book can be successfully used by students and teachers of both the physics and mathematics faculties of universities and pedagogical universities. It will also be useful for teachers of classes with in-depth study of mathematics for individual work with students interested in mathematics.