An introductory graduate course on supercomputing for computer science, applied science, and engineering majors is described. The interests of the students cover a broad range, from training as engineering or scientific supercomputer users to computer scientists interested an algorithmic, architectural, and statistical issues. An essential feature of this course is the w e of real supercomputer time on several machines of advanced architecture. Remote supercomputer access is obtained from the national supercomputing centers. The students do several small group research projects on supercomputers, concerning performance, algorithm design and applications. A number of techniques are wed to enhance the learning environment, such as local user guides, preparation for access dificulties, and appropriate beginning problems.