A complete digitized copy of the first edition of this book can be found at : www.archive.org/stream/flatlandromanceo00abbouoft

The story is about a two-dimensional world referred to as Flatland. The unnamed narrator, a humble square, guides us through some of the implications of life in two dimensions. The Square has a dream about a visit to a one-dimensional world , and attempts to convince the realm's ignorant monarch of a second dimension, but finds that it is essentially impossible to make him see outside of his eternally straight line.

The narrator is then visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland for himself. This sphere, who remains nameless, visits Flatland at the turn of each millennium to introduce a new apostle to the idea of a third dimension in the hopes of eventually educating the population of Flatland of the existence of Spaceland. From the safety of Spaceland, they are able to observe the leaders of Flatland secretly acknowledging the existence of the sphere and prescribing the silencing of anyone found preaching the truth of Spaceland and the third dimension. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste).

After the Square's mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth (and fifth, and sixth ...) spatial dimension. Offended by this presumption and incapable of comprehending other dimensions, the Sphere returns his student to Flatland in disgrace.
He then has a dream in which the Sphere visits him again, this time to introduce him to Pointland. The point (sole inhabitant, monarch, and universe in one) perceives any attempt at communicating with him as simply being a thought originating in his own mind (cf. Solipsism).

The Square recognizes the connection between the ignorance of the monarchs of Pointland and Lineland with his own (and the Sphere's) previous ignorance of the existence of other dimensions.
Once returned to Flatland, the Square finds it difficult to convince anyone of Spaceland's existence, especially after official decrees are announced - anyone preaching the lies of three dimensions will be imprisoned (or executed, depending on caste). Eventually the Square himself is imprisoned for just this reason.