Introduction.- Chapter 1. How to recognise a university.- Chapter 2. The media specificity of the university: a historical journey from the 12th century until the 20th century.- Chapter 3. The lecture: a collective study practice definitory for the classical university.- Chapter 4. The MOOC: the screen and its potential for making a digital university.- Chapter 5. On university thinking.- Concluding thoughts on the digital university, or the very possibility.