Part I of this chapter is a translation of the pages in Chapter 2 of my book Dimensions-theorie [1928,9] that deal with definitions in general and defining dimension in particular - passages often quoted by philosophers. In notes (added in bold-face brackets) I bring some of my views on the subject up to date. Part II is a reprint of sections of [1943, 1], a paper from an interesting series that L. R. Ford arranged in the class="EmphasisTypeItalic ">American Mathematical Monthly when he was editor of that journal. Each paper of the series had in the title a question beginning with the words What is… ? Ford asked me to answer the question for dimension. (As to the genesis of my ideas, See Chapter 21.) Part III summarizes some basic methodological ideas propounded in Chapter 1 of [1928, 9].