I have a Classics MA and I’ve been reading about mythology for as long I could read, so a book about a modern day Greek demigod going, essentially, to Demigod School is exactly the kind of thing I’d be all over. Part of me wishes I’d heard about Percy Jackson sooner so I could have read it as a kid. On the other hand, the fact that I first read the books in university for Classics meant that I could appreciate the mythological themes of the books on a much deeper level. That being said, most of the references are either fairly unsubtle or explicitly explained at some point, but Riordan has done enough of his homework to make references to some pretty obscure things.
In addition to clearly having done a whole whack of research into Greek mythology, Riordan is also a very good writer. Percy Jackson narrates his own adventures and Riordan does a very good job of getting into the mind of a twelve-year-old (given that he apparently wrote the books for his kids, that’s not really surprising). He has a sense of humour, so the story overall is pretty funny and lighthearted, though there are several times when things get pretty serious and/or scary and people start dying, but the level of violence or scariness never really surpasses something like Star Wars or the Marvel movies.
Percy Jackson should keep readers busy for a while. The series is five books like, and once the Greek mythology story is completed, Riordan also wrote a series based on Egyptian mythology and another on Norse mythology, as well as returning to Classical mythology again in related, but distinct series.
Also, the first two Percy Jackson books got made into movies (at this point, I have no idea if they intend to complete the rest of the series). They are, at the very least, entirely adequate. My biggest complaint about them is that they changed the main characters from preteens to twenty-somethings pretending to be teenagers.