The present paper is the outcome of investigations and theoretical analysts carried out for several years, aiming at an answer to the following questions: - what should the fund of the mathematics teacher's knowledge look like, within what scope and in what way should we convey this knowledge to him? In the commencing part of the paper, we analyze critically the existing system of educating teachers of mathematics; later, we present a proposal of a structure of five-year master's studies preparing the graduates for work in the profession of a mathematics teacher. Basing ourselves on the evolved criteria of choice of mathematical contents which should be considered indispensable in educating the teachers, we present a project of the minimum of knowledge of the fundamental subjects: mathematical analysis, algebra, geometry, probability and elements of statistics, theoretical arithmetic, logic and set theory, complex analysis, topology, differential equations, functional analysis, numerical methods, elements of computer science, the didactics of mathematics. Since the lecture at higher studies constitutes the basic form of conveying knowledge, the article closes with a discussion on modern ways of lecturing, activating the students. The scope of mathematical knowledge, proposed in the paper, which should be conveyed to the students - future teachers and the project of organizing the university teacher s studies can constitute the basic for the elaborating of the detailed curricula of such studies.