Fully distributed systems, typically termed Peer-to-peer (P2P) systems, seem to be of much more interest these days, especially moving from a pure file sharing use to a more commercial use and application. While the more traditional Client/Server (C/S) system belongs clearly to the distributed system, many new applications tend to prefer in certain cases a P2P-based approach. This lecture on "Peer-to-Peer Systems and Applications" outlines the major technology alternatives of P2P, introduces overlay networks, analyzes key P2P features, checks on implementation and deployability aspects, and investigates on scalability, efficiency, reliability, and commercial applicability. Search schemes, security mechanisms, and wireless use of P2P systems complete the overall P2P view. Based on a number of sample P2P systems the huge potential of them is outlined and applied in a challenge task in practical exercises. Students will get a deep insight into Peer-to-Peer systems and applications. In this context, the lecture will cover fully distributed communication paradigms to describe and evaluate alternative approaches to the client-server model. By means of basic concepts and approaches the students will learn, in which way the Peer-to-Peer (P2P) paradigm shows benefits as well as drawbacks in specific environments.