Set in the mid 21st century, this sci-fi novel, like Egan's later novel Diaspora, ties together many fascinating scientific and metaphysical ideas in a single book (The emphasis is very definitely on the "sci"). However, unlike Diaspora, there is a strong central theme underlying the story, a baffling idea called the "Dust theory". Any attempt to describe that theory here would be pointless, but I can say that it compels the reader to ponder some fundamental questions about the nature of reality. The theory is completely absurd yet not all that easy to refute. It has certainly caused me a few headaches... The dust theory is motivated and explained via another key theme in both this book and Diaspora - the concept of having a human "download" his mind onto a computer. Aside from the suspension of disbelief required in order to accept that such a thing is possible, Egan presents us with a well-thought-out and plausible scenario regarding these downloaded humans or "copies".
There are several other themes, of lesser importance, but fascinating in their own right, notably the "Autoverse": A piece of software that allows you to have complete control over your own virtual mini-universe - a world capable of modelling objects as complex as bacteria, down to the level of individual atoms.
Well that's the sci part. The human story behind all this doesn't have much intrinsic interest - the characters are vehicles for the ideas, and often one gets the impression that it is Egan who is speaking, not the character (they all seem to be uncannily good at making detached, intelligent comments on whatever is happening). This aspect didn't really bother me, as I think the ideas deserved some detached, intelligent commentary anyway.
The biggest flaw, I found, was the contrived ending. I won't go into details here, but needless to say, the dust theory turns out to be correct (in the story, at least). Once this is established, the author needs some kind of crisis with which to sustain the reader's interest, and it is this crisis, and the circumstances that brought it about, that I found to be rather contrived.
All in all though, I would definitely recommend Permutation City to any fan of "hard" sci-fi, or anyone interested in metaphysics or the philosophy of mind.