In Mathematics, topology is defined as the collection of all open sets in a space where it makes sense to talk about them. But over the course of last century, the study of topology has standardised itself by including discussions about the preservation and propagation of spatial properties like compactness and connectedness through continuous functions. Following that convention, the name of this entire book should have been the “Topology of Metric Spaces”. However, adhering to the literal meaning of the term, we will break from this convention and use this title only for the current chapter. In this chapter, we will explore open sets, closed sets, subspaces, sequences, and related concepts, following a similar approach as in the previous chapter—generalising these ideas, originally introduced in real analysis, to the abstract setting of metric spaces.