I remember reading somewhere that this is considered a classic work of science fiction, and that other writers, impressed with Abbott's story, have written spin-offs and sequels. This piqued my curiosity, and after Brent and Liz read it and had generally positive things to say, I decided to give it a go.
The main character of the book is A. Square, who lives in a two-dimensional world. Abbott spends a large portion of the book describing this world and the rules that govern it. Whit its rigid caste system and strict rules of social interaction, this "flatland" bears many similarities to British society during Abbott's time (the late 19th Century). A. Square has a dream in which he inadvertently wanders into a world that inhabits only a line. The world is governed by rules and social mores, just as the world in which A. lives. The inhabitants of the line world simply cannot comprehend that A. has more than one dimension. After a few unsuccessful attempts, A. gives up trying to explain it to them and simply leaves miffed and amused at their lack of understanding. However, when A. is visited by a sphere from a three-dimensional world, he fails to understand until the sphere lifts him up out of Flatland, allowing him to look on it from above. But A. soon realizes that he is unable to convince other from his world that his experience did, in fact, happen. Some of the older, more learned inhabitants of Flatland who remember events such as this happening in the past actively try to stifle A.
I suspect when Abbott published Flatland that it was rather controversial--it being, at least in part, a pointed satire of British society. However, this is not what intrigued me about the book. Neither was I taken with Abbott's writing style, which was quite utilitarian, like the writing of a mathematician who finally puts pen to paper on the novel that has been kicking around in his head for years. What Abbott is able to do is provide a clear example of how people deal with the unknown, often choosing to deify or to demonize that which they cannot comprehend.