The blurb begins: "Analogy is the core of all thinking." The authors then unload some 600 pages of support for this thesis, somehow making it both too vaguely general to be interesting and too pedantically detailed to be compelling. Hofstadter has finally written a boring book. I am sad to see the day.
The point is basically to identify analogies as being not just a literary device, but the way we categorize the world into concepts in our heads. "That's kind of like (X), in that (Y) acts like (Z), except..." A concept is a category -- not necessarily a category of things, but perhaps a category of situations or relations. (Even a lego-block word like "and" can be considered as denoting a category; contrast its uses with those of its near-synonym "but".) And what is a category but a bunch of things like each other in some way? --thus, analogies.
The authors go into mountainous detail: analogies behind single words, behind phrases and idioms, underlying our unconscious perception of the world, twisted in conscious wordplay; analogies discovered by children learning; analogies employed in creative work and scientific discovery. Analogies, analogies, analogies. Examples are deployed in battalions.
I feel that, for all the breadth and detail (and page count), there's not much depth here. If you're interested in the brief description of the Copycat toy problem ("abc->abd"), you'll really want to read Hofstadter's earlier Fluid Concepts (1995), which gets down into models and algorithms. If you're interested in how concepts translate between English and French (the book takes the opportunity to investigate its own construction), well, there was his 1997 book about translation. This book has a nice summary of the intuitive concepts that led Einstein to revolutionize physics in 1905 -- but if you're really into that, you'd want to read a book about Einstein, not this half-chapter.
It's not unreadable; there are points of interest. I like the definition of intelligence (both in the smart-people and AI-goal sense) as "the ability to pick out salient concepts" (or, if you like, to put new experiences into relevant categories). That feels nice and general, and the book provides a good base of support for it.
But nothing here is all that compelling. Or challenging. I guess if you're a Platonist then it's world-wrenching heresy, but I spent most of the book saying "Sure, no problem." If analogies are taken so broadly as to cover any kind of concept, then yes, analogies underlie all thinking. If all you have are tools, then everything starts to look like tool use.