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Teachers are in difficulty with regard to the space and emphasis to be given to set theory topics, in their preparation and in their work, because they have not been provided with adequate knowledge at the university. It is safe to say, on the basis of much experience, that the average mathematician, even the researcher, does not know what set theory is. Two prejudices stand in the way of a good knowledge of the theory: one, of a minimalist type, is its identification with an unspecified "set theory", an austere language that is too demanding if one wants to impose it prematurely; the other is of a maximalist type and consists in the supposed and effective link with the more subtle questions of the foundations of mathematics. But the theory has an important mathematical content, and with many implications of didactic interest.