The Research Experiences for Undergraduate Faculty (REUF) program of the American Institute of Mathematics prepares faculty to engage in research with undergraduate students, encourages long-term research collaborations among some of its faculty, and builds a network of faculty who supervise undergraduate research. Participants of each REUF workshop are faculty members from undergraduate colleges interested in mentoring students in research mathematics at their home institutions. During a workshop, senior mathematicians with experience supervising undergraduate research present open problems suitable for undergraduates. The REUF program also includes several follow-up activities.