Abstract
The article presents a multi-level system of subject Olympiads and competitions in mathematics for the identifi cation and development of mathematically gifted schoolchildren that has developed in Russia at present. The activity of each structural component and their purpose are described. The conceptual bases of work with mathematically gifted children in the multi-level system of subject Olympiads and competitions are revealed: the formation of the intellectual elite; increasing the role of mathematics in modern society; identifi cation, selection and self-realization of gifted children; professional orientation; development and specifi city of tasks for mathematical Olympiads and competitions; coaching support in working with mathematically gifted children; content and stages of work with mathematically gifted children; a variety of forms of additional education for mathematically gifted children; stimulating teachers to work with gifted children; organizational support of education management bodies; popularization of mathematical education.
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