 Cantor’s investigations into the properties of subsets of the linear continuum are presented in six masterly papers published during 1879–84, Über unendliche lineare Punktmannichfaltigkeiten (“On infinite, linear point manifolds”). Remarkable in their richness of ideas, these papers provide the first accounts of Cantor’s revolutionary theory of infinite sets and its application to the classification of subsets of the linear continuum. In the fifth of these papers, the Grundlagen of 1883, are to be found some of Cantor’s most searching observations on the nature of the continuum.