This article provides an introduction to the concepts and tools of kinship network theory as used by the other articles of this special issue. Based on the conceptual apparatus of graph theory, it presents the features of kinship networks and the techniques of their analysis in a non-mathematical language for social scientists (more formal definitions are given in an appendix). The fundamental notion of a "matrimonial circuit", a crucial element in the computerized analysis of marriage choices, lies at the heart of this approach. New methods of analyzing networks by means of networks, as well as a series of measures for evaluating the quality, gaps and biases of genealogical datasets are also included. All of the techniques mentioned are im...