First up is Edwin A. Abbot's classic Flatland: A Romance of Many Dimensions ... something that you might have encountered in one of the better highschools, even though it does "fall between the cracks" between math and lit ... it's the 616th "most popular" book over at LibraryThing, which makes it something along the lines of 1,000 times more likely to have been read by my readers than the typical stuff I flog in this space. This popularity is no doubt due to the venerable nature of the book (so that one's teachers' teachers' teachers might have read it), having first been published in 1884. Abbot was a clergyman, Shakespearean scholar, and school headmaster in Victorian England who had an avocation for mathematical theory. While messing with the concepts of dimensions (such as the 11-dimension worlds of certain types of "string theory") seems mainstream to today's reader, the book was rather revolutionary in its (pre-Einstein) era, and even coupled still-challenging dimensional visualizations with cutting social commentary.
The book is written from the perspective of (and was initially attributed to) a 2D-world entity "A Square" who has an encounter with a 3D-world entity (a sphere) that passes in and out of the 2D plane. In the course of the narration, the Square describes the things of his world, how social standing is determined (the number of sides, making the smooth curve of the circle presented by the sphere seem nearly divine), rules of behavior, and various hazards (the females are straight lines, being both nearly invisible and quite deadly if approached straight on).
The narrating Square has had strange dreams of one dimensional worlds, where he attempts to convince the reigning line segment of his multi-dimensional reality, and even attempts to deal with zero-dimensional point entities. These dreams seem to have been generated by the Sphere in order to give the Square some awareness of the 3D-world, which works for a time ... even too well, as the Square takes the realizations he's had of the Cube, and then begins (by extension) to query the Sphere as to 4D forms, which the Sphere stridently refuses to contemplate. When the Square tries to spread his gospel of higher dimensions, much chaos ensues, and he (and his closer associates) all end up destroyed or in prison.
Needless to say, Abbott puts together some still very challenging "thought experiments" about dimensional realities, framed within social/behavioral contexts on each level. It is, admittedly, as difficult for us to imagine 4-dimensional objects as it was for the Sphere in the story, so this book (even after 125 years) is as "fresh" on that level as the day it was written. Certainly, the "cultural" patterns detailed regarding challenging "authority" and the world-view of the masses have likewise not lost much of their value.
Flatland, I'm sure, is available in numerous editions. The one I have is one of those delightful "Dover Thrift Editions" which has a whopping $2.00 cover price (even though I picked up mine in a used book store for 50¢), so can be effectively used for one of those times when you're almost up to the magical $25 "free shipping" level at Amazon or B&N!