Naïve set theory, that is the theory of sets that assumes that we all regard a set as a collection of objects, is the topic of this chapter. This is certainly how most people think when they think about sets. We take this as our starting point and we introduce the notion of infinite set, only to discover how subtle even that first concept is. We then proceed to examine some of the paradoxes (including Russell’s Paradox) that will make it unavoidable to abandon naïve set theory, and accept the necessity of an axiomatic treatment.