Six students will participate in a Research Experiences for Undergraduates project focusing on mathematical problems in graph theory, finite groups and combinatorics. This constitutes the twelfth year (predating REU) in which undergraduate research in mathematics has been sponsored by the University of Minnesota- Duluth. Because of its successful history, problems for the activity come from all parts of the country - especially from former students and mathematicians familiar with its past accomplishments. Typical problem areas include determining circuits in digraphs, complete mappings of groups, labeling of graphs and Hamiltonian paths. Students are encouraged to publish their work. Fifteen papers were produced during the past year, written by REU students alone, as well as in collaboration with faculty. An active visitor program contributes breadth and vitality to the summer program. In addition to generous institutional support, the National Security Agency also contributes to this effort.