In Chap. 7 the theory of linear relations is presented. In Sect. 7.2 we study properties of linear relations, defined either by a range or by kernel representations. In Sect. 7.3 characterizations of the classes of dissipative, accumulative, selfadjoint and non-negative linear relations are presented. Formulas characterizing adjoint linear relations in terms of range and kernel representations are exhibited in Sects. 7.5–7.6. Transversality and disjointness of linear relations are studied in Sect. 7.7. In Sect. 7.8 connections between Nevanlinna families and Nevanlinna pairs are discussed. Certain invariance results for operator-valued Nevanlinna functions, as well as for Nevanlinna families, are given.