I would have to disagree on Rick Riordan not following the myths very well, even if you are Greek, I highly doubt that automatically qualifies you in the matter of Greek Mythology. Now if you have studied it or have been exposed to it a lot, which is highly likely, I'm sure, then by all means mention that. But your nationality has nothing to do with whether you know anything about the area's mythology. For example, I live in an area that was heavily populated by Native Americans, but I don't know a single thing about the local tribes culture (this is not a perfect example, sorry. Apples and oranges I'm sure). Granted, I should, it is important to US history, but still. I feel that he does have a very good understanding of classic Greek mythology, even if he takes license to change some things. These changes are necessary to the series because he is introducing completely new elements to the mythology as a whole. I think that it is because of his understanding of Greek mythology that he is able to make these changes to traditional ideas seem so seamless and smooth, at least to me. Every difference is explained in an, again, in my opinion, obvious manner. I do want to say that I was exaggerating when I said "phenomenal" writer. I'm just excited to finally have a new book to read. Phenomenal would be more like C. S. Lewis or J. R. R. Tolkien. However, they won't be writing new books any time soon.
Now, I realize that this qualifies me as an expert on Greek Mythology about as well as being born in Greece does, but I have read Edith Hamilton's "Mythology" and also The Odyssey and Iliad, among many other books on Greek and other mythologies, including Norse and Egyptian. This has given me a very good, working knowledge on at least the basics of Greek Mythology.
