When thinking about prepositions, always first think about their physical meanings. If a cat is ON a table, it means the cat sits directly on top of the table. If a cat is AROUND a table, it means the cat is not far from the table. Thus, "on" is more precise.

If it is a nonfiction book, you can say either and there's almost no difference in meaning. I think "on," as opposed to "about," suggests a systematic and complete treatment. "Euclid's _Elements_ is the classic book on geometry." "Babel: Around the World in Twenty Languages,' by Gaston Dorren, is about world languages. It isn't a formal book on linguistics. It's a series of entertaining essays in which he touches on a variety of interesting topics." If it is a novel, you might describe it as being "about X." I don't think you'd ever call it "on X." "'Tom Sawyer' is about a boy growing up in Missouri in the early 1800s."

There's not much difference. 'On' might sometimes be on a broader subject, whereas 'about' may be about a more specific topic, but generally, they can be used interchangeably.

I read a book on / about politics. (no difference).