The present chapter introduces Russell’s first theory of denoting, namely the one he put forth in The Principles of Mathematics and endorsed up until the time he struck upon the theory of descriptions in 1905. Two intermingled tasks are involved: one is to explain the distinctive features of the theory itself – primarily to facilitate the discussion in the following chapter. This will be done just about in full. The other is to introduce the broader theoretical setting in which Russell’s discussion of denoting is couched. Here I will merely point out some of the most salient features, without attempting to answer all the questions it gives rise to. Some of them will be touched upon at various points in the following chapters, but their more direct discussion will have to wait until Part III, after the discussion of Frege.