The Internet is a very large scale pervasive reality that is essential to all scientific, economic and social activities. It is constantly evolving and changing under the impact of new network technologies and new user demand and behaviour. This research course will bring together engineers, mathematicians and physicists to examine the Internet from a probabilistic perspective in close relation to reality and to the Internet’s expected future evolution. The objective is to identify and develop new mathematical approaches that can provide insight into the Internet’s expansion and organisation. The course will briefly review Internet protocols in the wired, wireless and sensor network domain, and discuss its projected evolution in view of current research initiatives throughout the world. The basis for the mathematical analysis of the Internet will be outlined in terms of queueing networks and random graphs, and insight via statistical mechanics will be provided. The course will then examine in detail issues such as self-organisation, criticality, system robustness and resilience to attacks, both in terms of analytic and algorithmic (protocol) considerations. New problems in probabilistic modeling of electronic agents will also be discussed. The detailed presentations will be complemented by presentations of ongoing research and with sessions where research problems will be formulated and discussed.