Mathematics education faculty working in mathematics departments are commonly involved in teaching undergraduate mathematics courses, teaching and supervising postgraduate students of mathematics education, and developing mathematics teachers (pre-service and/or in-service). This paper proposes a new elective course that can be taken by either undergraduate mathematics majors or by graduate teaching assistants pursuing degrees in mathematics and teaching undergraduates themselves. Twenty-eight topics are suggested, and the rationale for each is briefly described. Offering such a course provides different opportunities for students; for example, familiarizing them with effective ways to teach and learn mathematics, which has the potential to improve their effectiveness as tutors within the department. A similar course has been successfully taught to undergraduate students majoring in mathematics at an Iranian university for nearly two decades.