"Percy Jackson and the Lightning Thief" by Rick Riordan is about a 12-year-old dyslexic boy who learns that he is the demigod son of Poseidon, God of the Sea. In the book, Zeus' lightning bolt has been stolen and its up to Percy to get it back from the Underworld. There are many differences between the book and its movie adaptation "The Lightning Thief;" the intricate details of the character's lives as well as the reasons that Percy takes up the quest to retrieve Zeus's stolen bolt are completely different.
Percy Jackson is an awkward 12-year-old boy in the book, whereas in the movie he is 17 and played by the handsome 18-year-old actor Logan Lerman, who couldn't be awkward if he tried. In the book Percy has to learn who is father is, while in the movie everyone already knows that he is the son of Poseidon. In the book Percy doesn't own any electronic devices -- as they attract monsters -- whereas in the movie he owns an iPod Touch. In the book, his divine abilities and the identity of his father are revealed when he makes the water in a fountain attack Nancy Bobfit; in the movie, Percy can hold his breath underwater for an incredibly long time, and also manipulates water in ways that he does only in the later book "The Battle of the Labyrinth."
Grover and Annabeth
In the movie version, Percy's best friend, the satyr Grover, makes more wisecracking jokes based on archetypical satyr-like behavior of skirt-chasing and ogling girls. Annabeth, the tough tomboy and daughter of Athena, is 12 years old in the book -- not the curvy demigod Annabeth of the movie, played by Alexandra Daddario, a 24-year-old actress who practically smoldered whenever Percy came her way. In the book Annabeth had a crush on an older counselor at Camp Half-Blood -- not Percy, who is her friend and not a love interest.
What Lightning Thief?
The plot of the book revolves around Percy being accused of stealing Zeus's lightning bolt and subsequently having to go through a series of adventures to get it back, as he has to get permission from Chiron to embark on a hero's quest to search for the stolen bolt. In the movie, the lightning bolt is not the pivotal subject of the story; instead, Percy has to go to the underworld to rescue his mother.
The overarching metaplot -- the titan Kronos attempting to rise up and break out of his prison in Tartarus and take over the world -- that is a major part of the books is not even mentioned in the movie. Ares, God of War and his daughter, Clarisse have interesting roles in the book but are not featured in the movie either. The Gods wear normal clothes in the book, but in the movie are dressed in Greek armor or togas (except when they are around mortals).