Flatterland is sort of an unofficial sequel to Abbott's classic Flatland, written in modern non-Victorian English. Although Victorian English gave the original a pretty classy feel, Flatterland doesn't disappoint. Its aim is similar to that of the original: To explain new mathematical concepts to lay people in lay language.
The book succeeds brilliantly. It's filled with illustration to help visualize the concepts, and the stories around which the concepts are introduced are reminiscent of Alice's Adventures in Wonderland (well, the fact that chapters have names like The Topologist's Tea-Party and Along the Looking-Glass probably helps), and this gives the book a whimsical tone (that's a benefit). Here's a sample:
"Is Planiturth's universe built from mathematics? Or is mathematics built by the minds of Planiturthians? Planiturthian mathematicians would like to think that their universe is built from mathematics, but that's only natural, after all. Planiturthian physicists would like to think that the Planiturthian universe is built from physics. Planiturthian biologists would like to think that the Planiturthian universe is built from biology. Planiturthian philosophers would like to think that the Planiturthian universe is built from philosophy. (Let me tell you a secret: it is. The fundamental unit of the Planiturthian universe is the philosophon, a unit of logic so tiny that only a philosopher could hope to split it.)"
The book also ventures a little into physics, explaining things like the Schrödinger's cat, the double-slit experiment, time travel, and forces. But the meat of the book is mathematics.