Grid protocols and technologies arc being adopted in a wide variety of academic, government, and industrial environments, and there is a growing body of research-oriented literature in grid computing. However, there is a need for educational material that is suitable for classroom use. This paper describes our topics, exercises and experiences of teaching grid computing courses in the fall semester, 2004. to undergraduate computer science students at Lewis & Clark College and to a mix of undergraduate and graduate computer science students at the University of Arkansas. We identify a set of six knowledge areas that can help to structure course material in grid computing. In conclusion, we recommend that a grid computing course cover, or have as prerequisites, material on (1) remote method invocation and (2) security and certificates. Finally, student comments indicate the need for a series of grid programming exercises of increasing complexity.