The lightning thief
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The main conflict in the story is the disappearance of the master bolt and exactly who has stolen it. Percy is the main suspect in the theft because he is Poseidon's son, and he was in the right place at the right time.
Another recurring conflict is Percy's relationship with Luke. Although Percy is unaware that Luke is in fact a nemesis, we as readers garner this information early on.
The Lightening Thief