Percy Jackson - Young Percy is both the protagonist of the series and the narrator. When we first meet Percy in The Lightening Thief, he is a 12 year old student attending Yancy Academy, which is a private school for troubled kids located in upstate New York. Percy tells us that he likes to eat blue food, and that his mother gives it to him as often as she can as an act of defiance against Percy's Stepfather who once insisted blue food does not exist. We also learn that Percy has dyslexia and ADHD (Attention Deficit - Hyperactivity Disorder.) On his website, author Rick Riordan states that his own son has dyslexia and ADHD, and that he wrote the character of Percy with the same traits for his son's benefit.
Later, we learn that Percy is actually a demigod - the son of a Greek god (in Percy's case, Poseidon) and a human mortal. Additionally, it is explained that Percy's "dyslexia" is actually due to the fact that Percy's brain is wired to read the letters of Ancient Greek while his ADHD is really just his "battle-field reflexes" and heightened senses. (The Lightening Thief, p. 88)
Since Percy is a descendant of one of the "big three" gods (Zeus, Poseidon or Hades), his powers are more prevalent than those of other demigods. As the son of Poseidon, many of his powers revolve around water. He can breath underwater and control large amounts of it. For Percy, water also contains a healing power. Since it is said that Poseidon was the god who created horses, Percy has the ability to communicate telepathically with sea creatures, and animals or creatures with horse-like traits. In the book The Last Olympian, Percy bathes in the River Styx, which is located in the underworld. Like Achilles, he is then given immortality.
Grover Underwood - Percy Jackson's school friend. Percy is shocked to learn that Grover Underwood is actually a satyr sent to protect him against creatures who would do Percy harm. His official title is "Keeper," and it is his job to help find and bring worthy students to Camp Half-Blood.
As a satyr, Grover is half-goat, half-human. He has the lower body of a goat and the upper body of a human. He also has horns which are typically hidden by his curly hair. Although Grover is technically much older than Percy, satyrs mature at about half the rate that humans do - putting him right around the same age as Percy. Grover accompanies Percy to the Camp Half-Blood, and on all of the adventures Percy has after that. Like other satyrs, Grover is on a quest to find the god Pan.
Sally Jackson - Percy's mother. In The Lightening Thief, Sally is taken to the underworld by a Minotaur seeking to harm Percy.
Gabe Ugliano - Percy's step-father. Percy describes the man as a "world-class jerk" (The Lightening Thief, p. 30) and that he reeks of "moldy garlic pizza wrapped in gym shorts." (The Lightening Thief, p. 30) Later, we learn that Percy's mother married him because of this smell. It was he hope that the smell would ward off any creatures trying to find her son.
Mr. Brunner - Percy's wheelchair-bound Latin teacher. This is a pseudonym, however. Mr. Brunner is actually a centaur named Chiron. Chiron is the head instructor at Camp Half-Blood.