Internet and Grid-based systems, whether their purpose is computation, collaboration and information sharing, are all instances of systems based on application of fundamental principles of distributed computing. This paper reports on a graduate seminar on Internet and Grid computing which focuses on the fundamental principles and concepts of distributed computation which underlie Internet and Grid systems, both software and applications. The course takes a broad definition of Internet, and Grid computing, ranging across high performance computation to peer-to-peer file sharing systems. The focus is on identification and analysis of the concepts and principles underlying Grid computing and how they are realized and applied in systems ranging from Globus to Freenet with Web services in between. In summary, the course is a "what is it" rather than a "how to do it". Each participant does a project concerning an Internet or Grid computing subject and presents it to the class.