This research concerns the tension between collection and useful use of data and privacy. Collected data is either published in an adapted form or stored in a database where questions can be asked to a limited extent. The challenge is to do this in such a way that privacy is sufficiently protected, while at the same time the limited form in which the data is available is sufficient to derive useful information from data. A popular way to analyse this scientific issue is called Differential Privacy (DP). Here so-called non-asymptotic analysis methods from information theory are used to analyse DP.