The purpose of this article is twofold. In the first place it aims to give a general picture of the content and method of school mathematics teaching in a country in whose scientific and technical education the Western world is becoming increasingly interested. This general picture is here based entirely on publications of the Ministry of Education of the RSFSR (Russian Soviet Federal Socialist Republic) and on text- and other books in general use, mostly from the Russian Republic but a few from the Ukraine. It is not based on personal contact with the system or with teachers who have worked within it, but it is hoped to extend this article at a later date on the basis of first-hand experience. Aware of the diversity and flexibility of our own system of mathematics teaching, we would not expect a foreigner to understand it fully from publications alone. The Russian System, however, is less extensive and more unified, and we may therefore hope to obtain a useful understanding of it from books alone. We must remember, though, that it is in a process of change, and also that, as in England, there will be considerable variability from one school to another depending on the quality of the teachers. However oversimplified this introductory article may be, it should at least serve to give an orientation towards the subject.