I can't praise this book highly enough. I just wish I had more time to "mine" its depths.
The subject matter is maths, of course. But the approach puts the maths into the context of how it is used to solve real-world problems - giving an insight into the development of applied mathematics - often mistaken as mechanics and stats.
Korner's description of the people behind the maths, particularly Richardson, is very warm and helps you feel how particular problems were tackled.
The style is "literary" and the exercises, which are scattered throughout, "emerge" from the text. This provides real motivation for the problems - and motivates the reader to learn something by attempting them. It reminded me of Polya's classic "How to Solve It" (now that's an ABSOLUTE must).
I think Korner's target of a bright teenager is a bit ambitious. I feel the intended reader would have to be a pretty serious minded individual destined for the "premier division" maths departments to get much out of the book - but I may be underestimating the potential of the readers.