This REU site award supports six undergraduate researchers working under the supervision of the principal investigator. It continues a tradition of summer research programs conducted every year (except one) since 1977 by the principal investigator who often recruits former students to assist with the program. The quality of the work is exceptionally high, Of the forty-four students who have been through the programs, thirty-two have gone to graduate school, and twelve have already earned the Ph.D. Thirty-two papers written in the program have already been published, nine are in press and a dozen or more are under review and in preparation. The principal research theme of the program is discrete mathematics as reflected in problems from graph theory, combinatorics, finite groups and coloring problems. Problems often build on work done in previous programs, through correspondence with colleagues, and by searching journals. Each student is given an individual problem and a write-up at the end of the program is required. Students are encouraged to present their work at various professional meetings.