This booklet provides an overview of the Elements of Mathematics Program used in Project MEGSSS (Mathematics Education for Gifted Secondary School Students). It was designed for gifted students in grades 7-12 with excellent reading and reasoning ability. It attempts to explore the upper content limits of the mathematics that such students can understand and appreciate. An innovative feature is that some of the more advanced parts are not to be teacher-taught in the classical mode; students read several books on their own, with the teacher then leading a discussion of what was read. The contents of the program are listed, with a detailed description in an appendix. The role of logic and intuition, enrichment and acceleration, teacher preparation, and evaluation are considered, followed by some questions and answers about the Project. (MNS)