Surveillance is a social phenomenon that is general and commonplace, employed by governments, companies and communities. Its ubiquity is due to technologies for gathering and processing data; its strong and obvious effects raise difficult social questions. We give a general definition of surveillance that captures the notion in diverse situations and we illustrate it with some disparate examples.A most important, if neglected,component idea is that of the identity of the people or objects observed. We propose a general definition of identifiers as data designed to specify the identity of an entity in some context or for some purpose. We examine the ways identifiers depend upon other identifiers and show the provenance of identifiers requires reductions between identifiers and a special idea of personal identifier. The theory is formalised mathematically. Finally, we reflect on the role of formal methods to give insights in sociological contexts.