As one of our previous puppies, Nine Princess in Amber, The Swan Knight's Son and its sequels are books that were written as one (or so I have read.) Still, the first book in the trilogy can be read as it is, and it presents you with an enjoyable introduction to the world John C. Wright has created.
The first thing that should be mentioned is that the Swan Knight's Son is a young adult novel. It can also be enjoyed by er... senior readers, though, and, in fact, some of the references and themes the book touches may fly over the head of almost any teenager. Nevertheless, it is something that should be mentioned as it is a book that was clearly written with a type of reader in mind, and its style and form reflect that choice. Ultimately, it is an adventure tale, and you will not find many "adult passions" even if they are mentioned or hinted. Sex (or sexual passion) is more or less inexistent, and evil and good appear as functions of a metaphysical reality, not just material necessity or your average human tragedy. As most of the characters are not human (e.g. talking animals) or may not even exist in our reality (e.g. elfs,) their needs and goals are not always relatable even if they all are part of a human-centric cosmology.
Thematically, this is a coming-of-age story set in our world (contemporary America, in fact.) However, this reality is surrounded (besieged?) by another reality that constantly toys with humanity. That other world is pretty much a fairyland-like world, but one bound by the imperatives of a Christian and Biblical cosmology. The elfs, pixies, and other creatures that come from that dimension are not your average D&Dified races (in other words, just humans with pointy ears) but almost demonic entities thirsty for human souls.
To say that the book has christian symbolism would be an understatement. The Lord of the Rings may have a christian subtext, but in the Swan Knight's Son those elements are the story, and although you can ignore them, they cannot be removed from it. The Fall of Man, its redemption by Christ, and the Final Judgment are explicitly mentioned, and they are not mere fluff (although you may choose to read it as such.)
The elfs and other creatures that appear in this book are not merely evil because they are nasty, egotist, enjoy the occasional human snack, or are evil in any human/material scale but because they represent a metaphysical evil. It is pretty much implied they are fallen angels of some kind or, at the very least, servants of the Devil. Their wickedness is a function of that cosmology, and like the actors in a big play, they have a role to play, and their destiny is also preordained:
"They were born before Man with fish and fowl, on the second-to-last day of Creation and they shall descend into Hell on the first day of the second creation, when heaven and Earth are remade. [...] all will perish on the world's last day and be eternally damned. There is no redemption for them. They have no souls than can be saved,"
These are not mere orcs or other brutes that may appear in any other book. These are child-snatching, shapeshifting, transdimensional beings whose existential imperative seems to be to make things miserable for humans and damn their souls while at it if they can. And I use the word imperative because, as is common in many myths and legends, it does not seem like they have any choice in the matter (not that they would choose otherwise, though.) To put it into human terms: they do not do the things they do because they have interests, needs*1, or material temptations but because they MUST, not unlike a tornado MUST destroy. The weather analogy is not that far-fetched as in one chapter we discover that the elfs serve the Winter and Summer Kings, and their battles and contests will determine when the next winter will come (and none of the parts involved has the best interests of mankind in mind.) Also, most of the paranormal events and the creatures and their behavior seem to be somewhat tied to astronomical events, implying some of their behavior is more like a cosmic dance than actual volitional acts.
*1A snowmen mentions their kind needs to kidnap human women to reproduce, though.
That is the cosmological and moral background of the novel, and although you can choose to ignore it, it is always there. Therefore, the antagonist, the monsters, and the Evil our hero fights are not "creatures" as much as a principle or even a "force." This is what gives the elfs and the other creatures that fairy-tale, poetic, or mythical (or even alien*2) aura which makes them seem human (because they speak and think) and inhuman at the same time. Humans create a purpose by existing, doing, and choosing between options (or, at least, that is how we see it from our perspective) but these strange beings are a purpose which, again, it is dependent on the bigger cosmology already mentioned.
*2Literally. In fact, there is a subset of heretics in the already quite wacky camp of ufologists that claims fairytale creatures and alien "visitors" are essentially the same beings but under different masks.
In a more formal aspect, the book is easy to read, somewhat short, and meant to be a page-turning. In fact, it seems to have been designed to accomplish exactly that as the book is divided into a great number (62, if I am not mistaken) of mini-chapters. As I have not read anything else from John C. Wright, I do not know if that is the usual arrangement for his books, although I speculate it could be a consequence of how he meticulously plans his books ( he does not look like someone who writes by the seat of his pants.) Personally, I would have preferred the broader classification with just ten chapters, as some of the mini-chapters where too short and occasionally the action seemed to jump from one place (or time) to the other when a smoother transition would have been better.
I recommend reading this with your preferred encyclopedia nearby. Every time you find a peculiar name, if you google it, you will find it is a reference to one legend or another. Nathan Housley has already linked to bigger and more detailed analyses of such influences and references, so it would be pointless to say more about it.
Plot-wise, this book is an introduction that follows the protagonist (Gilberec Parzival Moth, or just Gil) trying to make sense of his weird life, his mysterious ancestry, and his desire to become a knight. That desire would have been Quixotic in any other setting (and, to be fair, it still is a bit of that in this one) but the windmills are real this time and, well, the world always needs a few knights.
It is the "discovery & training" book, if you will, where Gil finally understands (as much as these things can be understood) the nature of the strange reality that surrounds him, trains and gets stronger (thanks to a hardcore routine of bear-wrestling,) and finally finds a worthy challenge to test his skills and his mettle. Notwithstanding all that bear-hugging and the magic weapons he later finds, the guy seems a bit overpowered for a teenager, and I do not know where he learned to use a sword. I mean, in one occasion he beats a few elfs (while wielding an improvised club,) transdimensional and almost immortal half-demonic beings with centuries of experience. I think that moment weakened the aura of fear and preternatural power surrounding the elfs that Wright had managed to craft in the previous chapters.
Still, he is a half-human of sorts and, besides, this a young adult novel, and their protagonists are usually of the Chosen One variety. In any event, and comparing it with other books, I liked that the protagonist had to pass a grueling and brutal training regime, which somewhat justifies his later exploits. Also, those training chapters and the other ones where he talks to animals were my favorites.
I cannot finish this short analysis without mentioning against what this book was written. All books have a purpose of sorts, even if it is just the evocation of a complex emotional experience, but it is also not uncommon that they have an "enemy." I do not think I am assuming too much if I say The Swan Knight's Son was written against some of the modern trends in fantasy and fiction. It is also an obvious jab at secularism and its anti-Christian ethos. Although I would not go as far as to say this is a "message fiction" book, it does have a few things to say. Inevitably so, of course, considering my previous comments about its cosmology. I do not know about other people, but I smiled at the implication that elfs and supernatural forces were behind secularism, and the image of immortal elfs conspiring to remove Christmass trees and replace them with Kwanza trees was quite hilarious.
The lack of religious substance in contemporary fiction has been a pet peeve of mine for a long time, especially when in most fantasy settings it SHOULD be there. Even if, personally, I find some elements of Wright's cosmology a bit constraining, as they seem to reduce the supernatural antagonists almost to the level of objects or symbols, it is a welcome difference nonetheless. I think the next book in the series deals with the elfs in more detail, so some of those issues may disappear.