The book consists of three parts .. The first part is devoted to mathematics, which arose either before classical Greek mathematics, or simultaneously with it, but independently of it. We are talking mainly about the mathematics of Egypt, Babylon, India and China. The second part is entirely devoted to three famous problems of construction - doubling the cube, trisection of the angle and quadrature of the circle. The study of these problems occupies a prominent place in the heritage of ancient Greek mathematicians. The third part describes the most interesting geometric problems encountered by Euclid, Archimedes and Papp. The geometric problems discussed in the book make up the bulk of what is known about the mathematics of the Ancient World. Beyond the book were only two important sections of ancient Greek mathematics - the arithmetic of Diophantus and the theory of conic sections of Apollonius. The book is addressed to schoolchildren, teachers and anyone interested in mathematics .