Our lives are facilitated and mediated by software. Thanks to software, data on nearly everything can be generated, accessed and analysed for all sorts of reasons. Software technologies, combined with political and commercial ideas and practices, have led to a wide range of our activities being monitored, which is the source of concerns about surveillance and privacy. We pose the questions: What is monitoring? Do diverse and disparate monitoring systems have anything in common? What role does monitoring play in contested issues of surveillance and privacy? We are developing an abstract theory for studying monitoring that begins by capturing structures common to many different monitoring practices. The theory formalises the idea that monitoring is a process that observes the behaviour of people and objects in a context. Such entities and their behaviours can be represented by abstract data types and their observable attributes by logics. In this paper, we give a formal model of monitoring based on the idea that behaviour is modelled by streams of data, and apply the model to a social context: the monitoring of web usage by staff and members of an organisation.