This book has been written mainly for high school students, but it will also be helpful to anyone studying on their own whose mathematical education is confined to high school mathematics. The book is based on a lecture I gave to Moscow schoolchildren of grades 7 and 8 (13 and 14 years old).
In preparing the lecture for publication I expanded the material, while at the same time trying not to make the treatment any less accessible. The most substantial addition is Section 13 on the ellipse, hyperbola and parabola viewed as conic sections.
For the sake of brevity most of the results on curves are given without proof, although in many cases their proofs could have been given in a form that readers could understand.
The third Russian edition is enlarged by including the results on Pascal's and Brianchon's theorems (on inscribed and circumscribed hexagons), the spiral of Archimedes, the catenary, the logarithmic spiral and the involute of a circle.