This is an amazing book by Douglas Hofstadter
. Most obviously, it is a book about Godel's theorem
. This is introduced early in the book, the explanation (as technical as any non professional mathematician is likely to want) is at the heart of it, and analogies and ramifications are approached from different angles to the very end.
The author has woven many things he loves into this book, including lighthearted fiction and music and art. All of these enable him to approach Godel's theorem from different directions again and again without boring the reader - in fact being much more interesting than an ordinary explanation. By the use of puns and many more subtle mechanisms, the author makes many connections between seemingly unrelated things in our minds.
Artificial intelligence is a major theme of this book, as are computers and computer programming - and intelligence in general. Self reference and meaning recur again and again, becoming connected in our minds to the art of M.C. Escher, which sometimes almost succeeds in referring to itself in a fashion no two dimensional picture can. Read the book, there are many beautiful reproductions of art included.