From the top:
The best writing about Philip Pullman and his work (by someone other than him) that I've found so far is Lauren Shohet's "Reading Dark Materials." A relatively short essay, it articulates an endlessly fruitful interpretive approach to the original series, and to Milton's Paradise Lost, for that matter. (See a fuller review here.)
To my knowledge, the best book-length treatment out there is Laurie Frost's His Dark Materials: The Definitive Guide. This encyclopedic survey carries an appreciative foreword from Pullman: "I can't recommend it too highly to the reader who's found anything interesting or enjoyable in this story of mine. I know I've returned to it frequently during the writing of the book I'm doing now, and I know I'll continue to do so." An inexhaustible trove for writer and readers alike, then.
A balanced, insightful critique of Pullman's theology, blended with admiration for his story, comes from Tony Watkins in Dark Matter: Shedding Light on Philip Pullman's Trilogy HDM. Incorporating his own remarkable interview with the author, as well as generous references drawn from the mass of source material already out there by 2004, Watkins does a tremendous job laying the groundwork for several major lines of inquiry. If he had spent less time on summary and biography, useful in themselves but probably not requisite for readers of the series looking for the analysis he stands poised to provide, he would have been able to give greater space to exploring themes like daemons and Dust and the handling of science in much more depth. As evidence of his acumen, I include a few examples:
"Now 'Lyra had to adjust to her new sense of her own story, and that couldn't be done in a day' (p. 130). There are echoes of Pullman's own story here. He started writing The Golden Compass in the early 1990s, sometime around, or soon after, the death of his mother. It was while he was subsequently sorting through her papers that Philip unearthed things about his parents that he had never known. His discoveries were not on the scale of what Lyra is told, but something of the same reorientation of perspectives must have taken place." (67 cf. Pullman's biographical sketch I have a feeling this all belongs to me; also Iorek's words to Will, cited Watkins p 88: "'If you want to succeed in this task, you must no longer think about your mother. You must put her aside. If your mind is divided, the knife will break' (p. 194)." )
"There's a book [mentioned in Lyra's Oxford] on 'some curious anomalies in the mathematics' of the Four Books of Architecture by one of the world's greatest architects, Andrea Palladio (originator of the Palladian style). The book is by one Nicholas Outram--these are Philip's middle names." (101)
"Incidentally, Lord Asriel's comments about this verse [ie, Gen 3:19]--that the translation is disputed because the text is corrupt, and that it could mean God is admitting his own sinfulness (GC, p. 373)--are unjustified. I have yet to find any commentator arguing for an alternative translation of 'to dust you will return.' [his endnote: Some commentators do disagree with the majority in that they take 'to dust you will return' as something that was always inevitable for Adam, even before his rebellion. In other words, he would have died whether he sinned or not, and the judgment on him is that work will now be difficult for him until that time. Most see physical death as being part of God's judgment and a consequence of being expelled from Eden. But this difference of opinion is over what the words imply, not over the translation itself. See Gordon Wenham, Word Biblical Commentary...] And the idea that this could have any reference at all to God's nature has no basis whatsoever outside Pullman's fictional world." (123)
"When I asked Pullman to explain what he meant by 'interrogating the universe,' [from an interview with Charles Brown, at this defunct link], he replied [by email]: 'Perhaps "interrogating" is too fierce a word (not least in view of the pictures we've seen from Iraq recently [presumably from US soldiers humiliating and/or waterboarding prisoners]). I should have said something like "respectfully questioning." Human beings have got lots of ways of doing this; as well as the ones I mentioned, there is astrology, palm-reading, etc. I don't think these things give true answers; but what they might do--especially the more intellectually complex or enigmatic ones--is help you focus your question more precisely. So the answer you seem to be getting from them is actually coming from you. Probably.'" (136)