I recently was lent this, and, although I was apprehensive at first (it's a favourite amongst math students apparently), now I've read it I can't stop telling people about it.
It's the story of A.Square, who lives in the 2D world of Flatland. The first part of the book consists of him describing life in Flatland, how the triangles are the lowest in the social order (aside from women, who are but straight lines and therefore highly unintelligent), how they recognise each other, how they school their children etc. The rest of the story takes place in three other worlds: one dimensional 'Lineland', three dimensional 'Spaceland' and zero dimensional 'Pointland'.
Aside from being a critique on Victorian society (this was written in the late 1800's), it is also an exploration of mathematics and physics, questioning what a fourth dimension would be as well as going into great depths about angles and geometry.
HOWEVER, if that's not really your cup of tea (as it isn't mine), fear not, as aside from being deep and meaningful it is also written really really well, and in parts it is very funny. In short, this was one of the most refreshing and amazing short stories I've ever read: get on it.