This manual provides a systematic presentation of the in-depth course of planimetry. Along with the basic geometric information included in the standard school program in geometry, there is a large additional material that expands and deepens the basic information. The style of presentation adopted in the manual is markedly different from the traditional one: the theorem is a proof. In some cases, the authors do not formulate theorems and axioms in advance, but look for their formulation together with the reader. This approach is explained by the desire of the authors to give an idea of how mathematics is built and how mathematicians work. The book pays considerable attention to Lobachevsky's geometry, constant-width curves, isoperimetric problems, and proves a number of remarkable theorems of planimetry. The manual is aimed at students with an increased interest in mathematics, as well as everyone who is attracted by the beauty of geometry. It can be used in classes with advanced study of mathematics, in the work of mathematical circles and electives, serve as the main textbook in schools of physical and mathematical profile.