The first section of the book surprised me because it was very harsh towards women. I told my wife that it might be satire, but it was some of the worst satire I had read because it was so harsh. I've read a little satire and I really enjoyed Gulliver's Travels, Alice in Wonderland & Through the Looking Glass, and Animal Farm. The satire in those others was funny, but here it was just so unapparent that the book seemed mean or harsh. It is supposed to be satire of the Victorian Era and especially how women and the priesthood were treated and if the satire is even fractionally correct then I understand the neglect of women and the need for the suffrage and women's rights movements all the more, but for me at least I had to be told it was satire it was not apparent.
After the world of Flatland is setup then the square telling the story visits Lineland in a dream (a world of 1 dimension). After failing to get the king of Lineland to understand the 2nd dimension he wakes up from the dream where he encounters the same problem where he is now the shortsighted one. A Sphere from Spaceland comes and talks to the Square and eventually takes him to Spaceland where he can enjoy 3 dimensions. Later they together visit Flatland and Pointland (a land of no dimensions with one inhabitant). The square also inquires to the existence of extra dimensions beyond that which were not recognized in 1884 when the book was written. In 1905 Albert Einstein suggested that time was the 4th dimension and that we live in space-time. It was later that this idea was compared to the book Flatland and the book became popular again. Now of course, with theories like String Theory that surmise we live in a Universe with even more than 4 dimensions (all versions require at least 10 and up to 26 dimensions) the idea that there are dimensions we can imagine and mathematically calculate, but probably can never conceptually understand is an important lesson to learn- even if it turns out that String Theories are incorrect.
The really nerdy will call this classic a work of mathematical fiction rather than science fiction. To be honest part one is really slow and it hard to get through especially since the culture being parodied is far enough removed from us, and furthermore the humor in the satire is lacking which just makes it sad. But if you can make it to part 2 the book is well worth the read (and to be honest if you started at part 2 you would follow most of it except the layout of this house and the hierarchies in his societies politics). I'm glad to have read the classic, but it is not one that I will return to again.