Some of the reviewers here seem not to have read a great deal else in this field and I strongly recommend that anyone reading this book does not take what is written here as all there is to say.
It is a good book on the workings of the brain with an interesting bundle of hypotheses on how these working may generate conscious thought processes amongst other things. It is well worth reading so please don't take my criticisms as implying in any way that it is a bad book or poorly written. However, like all specialists writing partly outside their field it has limitations. They even acknowledge these limitations on occasion but there is a kind of magician's "sleight of hand" as there so often is with scientists working on brain functioning since they categorically state that dualism is false whilst refusing to go into the debate on qualia to any depth.
What it comes down to is that there is actually no explanation for consciousness here, just a possible direction for establishing a workable NCC framework. Even a fully explicit NCC framework would probably still not properly explain consciousness. At best it would explain it away and that explaining away may fall very short of a proper explanation for what is, after all, the only thing a sentient creature is really certain of - being conscious.
This is a very complex issue (or it has been made into one) and I recommend reading David Chalmer's 'Character of Consciousness' before you make up your mind on this book's more categoric statements about dualism and other philosophical issues (they are not philosophers and they wrote this book prior to Chalmer's book so let's be fair to them on that). Dualism may not ultimately be valid, certainly Cartesian dualism has few adherents nowadays outside of those who don't think much about it at all, but dualism has NOT been disproved and David Chalmers will show you why in clear precise logical terms. Also bear in mind that Edelman and co are amongst those criticised by Bennett and Hacker for using psychological predicates inappropriately and that debate is well worth looking at too.
I'd also recommend reading anything by Antonio Damasio, Peter Carruthers and Andy Clarke as well as Jesse Prinz (Gut Reactions)and Nicholas Humphrey (Seeing Red). The Philosophy of Mind collection of papers edited by David Chalmers is also excellent and contains Nagel's famous 'What it is like to be a bat'.
I know that even great scientists like Stephen Hawking like to say that science rules and philosophy is dead. Please don't be fooled by this arrogant stupidity as it certainly is not true in the field of philosophy of mind. Even if the only role of the philosopher was to insist on a proper and full explanation for consciousness as opposed to an incomplete reductionism that would be a very important contribution. As far as I can see, David Chalmers is prepared to go on pressing that sore spot in the explanatory gap for as long as it takes. Scientists can either pretend he doesn't exist or respond intelligently to the challenge he is making. Let's hope they go for the latter and ideas such as those in this book come to be framed in a way that takes account of both the scientific evidence and the philosophical requirement of a complete explanation that includes the how and why of the arising of subjectivity.