I am again reviewing this entire series in one go, because there isn't so much to say individually about the books.
These are really solid young adult fantasy books. I would recommend them to most fans of young adult books generally! They are better than the movies, so far, although I have enjoyed the movies.
The Percy Jackson books follow the story of Percy Jackson, a son of the god Poseidon, as he figures out who he is, tries to stay alive, and has adventures which culminate in an important battle. It's VERY young adult in terms of the way the characters talk (cheeeeeeesy dialogue) but the story and characters are more universal.
Unlike some young adult books I could mention, these books tread very lightly on teen angst, romance, and love triangles. Some of that stuff is there, but it's masterfully subtle and doesn't take away from the story. Any romance stuff is extremely secondary to the children of gods, saving the world adventure stuff. Which is awesome! The romantic-ish relationships between the characters are handled really well. They add a little bit of depth, but are not dwelt on. That aspect was handled really well.
These are very clean, light young adult books. Some other series purporting to be for kids of young adults have really dark or disturbing elements. Not these. There are villains, and violence, but it's tasteful and mostly about good people trying hard. They seem unusually uplifting and positive for the genre.
I would not hesitate to recommend these books to anyone (even young readers) who found the cheesiness inherent to young adult books acceptable.