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This paper is intended to give a brief survey of the use of surnames as a method to investigate issues in historical demography. After highlighting the importance of the reliability of the research sources and the need for the development of critical analyses, several statistical methods are described, most of which have been derived from population genetics and from quantitative approaches used by medievalists. These methods provide a way to describe the distribution of surnames, as well as to compare various distributions obtained successively through time and gathered from diverse areas in order to draw conclusions about the population dynamics, and particularly, about the geographic mobility of people over time. Several examples are given to illustrate this purpose.