The 1959 Royaumont seminar "New Thinking in School Mathematics," having agreed on the need for modernization, recommended that a second group of experts work out detailed synopses of the entire subject matter of secondary school mathematics. This book is the report of the second seminar and contains the Dubrovnik Program which stimulated much curriculum development in Europe at the beginning of the last decade. The seminar concentrated on the needs of the most gifted students (the upper half of the European Lycee or Gymnasium). Synopses for algebra, geometry, and for probability and statistics are presented in two cycles, the first for ages 11-15 and the second for ages 15-18. A statement of the goals and prerequisite mathematics precedes the list of topics recommended for each subject in each cycle. This is followed by commentaries clarifying the spirit and scope of the newer topics. The major commentaries cover: the role of the theory of sets in secondary school mathematics; teaching first-cycle geometry to provide experience of a wide variety of concepts and properties, leaving their logical arrangement to the second cycle; groups, rings and fields; vector and linear algebra; axioms for affine space and for the affine plane; and the development of probability and statistics. Some aspects of the teaching of calculus are reviewed in an appendix. (MM)