Flatland is a novel written by an 1800s geometry teacher to help explain some geometry basics to his pupils, or so it seems at first. The author, Abbott, then quickly goes on to some wacky 'what would a fourth spacial dimension' be like thinking. I'm still not sure if the rapid progression from mindlessly simple stuff to more difficult stuff is 'cause it fits the character of the speaker (A. Square) or if Abbot and I just disagree fundamentally as to what's hard to visualize.

Regardless, it's a good (short) novel if for no other reason than it's fun to try to come with with futher supposed characteristics of the fourth dimension as extrapolated from the first three. That and if you read the preface you get to see someone defending himself from Political Correctness attacks as far back as 1885.

I recently managed to find the full text on-line, and as the work has long since gone into public domain I've mirrored it.

Also worth reading is the 1960's sequel, Sphereland, which puts the world of Flatland on the surface of a sphere and shows how a lot of Einstein's general relativity comes into being. Sphereland then goes on to put our world on the surface of a hyper-sphere (or ball) and plays around with that for a while. That and a severe overhaul to the 1880 social attitudes makes for another good read.