I also recommend A.K. Dewdney's The Planiverse, published in 1984. It tells the story of computer science students who communicate with denizens of a 2D world. The diagrams and graphics are delightful.
I read it when it came out (I was 13) and it's one of the reasons I entered computing.
Another great book from a similar period: The Devil's Dictionary by Ambrose Pierce - http://www.gutenberg.org/ebooks/972 - Definitely one to have in the toilet.
If you're thinking of getting the annotated version, another classic in the same spirit is The Annotated Alice by Martin Gardner. It exposes a lot of double entendres, mathematical games, and other historical stuff about Alice in Wonderland that shows how much of a playful mathematician Lewis Carroll was.
Flatland is a great little book, highly recommended. It's from a time when writers would stop when they had no more to say instead of being paid by the word or to fit a particular format so don't be surprised by how much stuff is crammed in to it's 100 pages, if it were released in 2011 it would surely be 300 pages at a minimum, and it would lose a lot of its power because of that.
I read it recently. Great short read. Extremely sexist, but I guess it's a book of its time. Got me thinking hard about higher dimensions for a while, until my head started hurting :)
I´m pretty sure that´s part of the point of the book; in addition to the obvious, it is also social commentary on views on women at the time of its writing.
for a citation, the preface to the second edition includes this:
[A. Square] has himself modified his own personal views, both as regards to Women and as regards the Isosceles or Lower Classes...But, writing as a Historian, he has identified himself (perhaps too closely) with the views generally adopted by Flatland, and (as he has been informed) even by Spaceland Historians; in whose pages (until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration.
In the preface to Flatterland, a sequel of sorts, Ian Stewart explains that ¨Abbott was, in fact, a social reformer who believed in equal education opportunity for all social classes and genders; Flatland´s narrow-minded social system is his cry of frustration¨ as he wished to ¨satirize the rigid social structure of Victorian England...especially the lowly status accorded to women.¨
I found this book to be quite tedious. The whole class analogy (a satirical story line in which many-sided polygons are regarded as more refined than, say, triangles and squares) was just unbearably long-winded to me. I've read the whole critique so many times before.
And the notion that the reader will appreciate the three-dimensional space we live in (or 4-dimensional space-time, if you're like that) by going through a novella-length treatment of a 2d world...did not work for me, let's just say.
If you like the book, and many do, I'm glad. But it's not unanimous.
http://www.flatlandthemovie.com
The full length 95 minute one is less favorably held.