This updated handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entries in fairs and competitions. The use of projects to arouse interest in mathematics is noted to have been slow to materialize in this country in spite of the growth of science fairs and renewed emphasis in mathematics since World War II and the Russian-American rivalry in space exploration. Presented are directions on developing a mathematics project, titles of projects displayed in the past, ideas for reports and projects, leading questions, unsolved problems, and outlines of general topics suitable at the junior and senior high school levels. In addition, the document contains an annotated bibliography of mathematics books and periodicals and provides the names and addresses of mathematics-oriented publishers and periodicals. This revision, besides updating the references, has an added section on calculators and mentions women in mathematics, amateur mathematicians, and the history of statistics. The section for ideas for reports and projects has also been expanded. (MP)