The story opens with our protagonist (Square) explaining the realities of day-to-day living in - and the history of - Flatland: a two-dimensional world inhabited by line segments (women), and polygons of varying sides (men), whose numbers of sides dictate their social status within the domain. On New Years' Eve, 1999, two-dimensional Square - a four-sided member of the caste of professionals and gentlemen - finds himself in the midst of a dream about a one-dimensional world (Lineland); a world inhabited by what he refers to as 'lustrous points'. While he can see them, they cannot see him - at least, not in his true form. Rather, they observe him only as a line with a set of terminal points. Brought before the monarch of the realm, he vainly tries to express the realities of a life lived in a second dimension of reality - to no good end. Further on, Square is paid a visit by a three-dimensional sphere. Much like his own plight in the land of one dimension (Lineland), Square sees Sphere as a circle within his own land of two dimensions (Flatland). After much back and forth with Sphere, Square finds himself in a three-dimensional world (Spaceland). Sphere continues to visit Square at the passing of each millennium. With each visit, a new Apostle is brought forth to be introduced to the concept of the third dimension.Unbeknownst to the lower-castes of Flatland, their leaders acknowledge that the Sphere is, in fact, extant. Yet, they'd prefer to keep it a secret from the general populous. To keep the matter at bay, many witnesses are killed or thrown into prison - ultimately punished according to their social caste. Among those eventually imprisoned is Square's brother. As the concepts of multiple dimensions expand, Square tries in vain to convince Sphere that a fourth dimension is possible. In response, Sphere returns Square to Flatland in utter disgrace, frustrated that Square would so fiercely entertain such a wild notion. Square's return is soon followed by a dream, whereby Sphere shows Square a new dimension - Pointland - inhabited by a single point, who is the lone inhabitant. More correctly, Point is the only life, the whole universe, and encompasses everything comprising the strange dimension of Pointland. Throughout the work, we see minds being opened to new concepts and ideas, but also showing the limits of thought - and need for control - that often plagues scientists, big thinkers, and society as a whole. In the end, Square comes to parallel the ignorance of the monarchs of Pointland (and Lineland) as akin to his own (and Sphere's) previous ignorance of the existence of higher dimensions. Square, after much contemplation, decides to write the book that is to become 'Flatland' (this book). He writes it in the form of a memoir of sorts, hoping that someday - just perhaps - the next generations of Flatland will be visionary enough to take his work at face value, and to explore the idea that the Universe is often far more than it seems to a lone observer.