Volume One was begun as the first contribution, by the German section of the International Commission for Mathematical Instruction, to the topic of the scientific foundations of instruction in mathematics, which was one of the topics chosen by the Commission, at a meeting in Paris in October 1954, in preparation for the International Congress of Mathematicians in Edinburgh in 1958. Originally we kept chiefly in mind the needs and interests of the instructor in mathematics, but as our cooperative effort continued from year to year, it became clear that the material in our book was equally important for mathematicians in science, government, and industry. For the best realization of our general purposes, each chapter has been written by two authors, one of them a university professor, the other an instructor with long experience in teaching. In addition to these specifically named authors, of whom there will eventually be more than one hundred, from Germany, Yugoslavia, the Netherlands, Austria, and Switzerland, important contributions have been made to each chapter, in joint semiannual sessions, by the other members of our large group of coworkers.