The book of American mathematicians, in an accessible, entertaining and systematic form, illuminates a wide range of issues that find application in various fields of mathematics (algebra, geometry, number theory, computational complexity), but also in various applications: information transfer and storage, field theory and superstrings in physics, crystals and quasicrystals in chemistry. For mathematicians of various specialties: from algebra, geometry and number theory to cybernetics, coding theory and crystallography, for graduate students and university students.