Is reading Greek mythology allowed? For example, the Percy Jackson series? I think there are some verses of the Bible that talk about mythology (I Timothy 1:3-4;4:1-8; and II Timothy 4:2) But can you read about mythology if you don't believe in it?
The myths condemned in the Bible were teachings of people's imagination that were treated as real. Fantasy stories are not wrong in themselves but they can be wrong for the things they depict. See:
What makes some fantasy stories wrong?
I've read some of the Percy Jackson series. They aren't great fantasy, but all right. Morally, I didn't like how often Percy lies and it comes across as "necessary" instead of wrong. He also spends a lot of time going against those in authority (not just the bad guys).
Greek mythology as a whole has its own danger. The original myths are filled with their gods doing all sorts of evil, including fornication and adultery. They are presented as if evil is acceptable. To be aware of the Greek myths is not wrong, but there are a number of stories that are best skipped.