Uspensky V . A. What is non-standard analysis? - M. : Science. Gl. Red. phys. -mat. lit. , 1987. - 128 s. In the second half of the 20th century, so-called non-standard analysis appeared in mathematical science. His proposed approach to the justification of mathematical analysis is based on the assumption of the existence, in addition to ordinary real numbers, of infinitely large numbers and of infinitely small numbers. The full logical justification for this approach is quite complex and relies on the construction of mathematical logic. The purpose of the book is not to give a full justification, but only by postulating the necessary facts, to explain with available examples what is the essence of non-standard analysis For persons who possess mathematical analysis in the first year of university .