If You Liked The Lightning Thief 
by Rick Riordan…

…you might also like:

The Warrior Heir   by Cindy Williams Chima
After learning about his magical ancestry and his own warrior powers, sixteen-year-old Jack embarks on a training program to fight enemy wizards.

The Merchant of Death   by D.J. MacHale
Bobby Pendragon is a seemingly normal and somewhat reluctant 14- year-old boy who is swept into an amazing five-year quest.   (Pendragon; Book 1)

Artemis Fowl   by Eoin Colfer
When a twelve-year-old evil genius tries to restore his family fortune by capturing a fairy and demanding a ransom in gold, the fairies fight back with magic, technology, and a particularly nasty troll.

Dark Lord of Derkholm   by Diana Wynne Jones
Derk, an unconventional wizard, and his magical family become involved in a plan to put a stop to the devastating tours of their world arranged by the tyrannical Mr. Chesney.

…and these mythology-related stories:

The Minotaur   by Tom Mason
While searching for clues to his dad's disappearance, Alex finds himself transported to a world of ancient myths. Sent to ancient Crete to be a sacrifice to the horrific Minotaur, Alex must defeat one of the fiercest creatures in all mythology.   (MythQuest; Book 1)

Jason and the Gorgon's Blood   by Jane Yolen
Jason, who will grow up to become the head of the Argonauts, leads five other boys on a dangerous quest to save the kingdom of Iolcus, learning along the way what it means to be in command.

Odysseus in the Serpent Maze   by Jane Yolen
Thirteen-year-old Odysseus, who longs to be a hero, has many opportunities to prove himself during an adventure which involves pirates and satyrs, a trip to Crete's Labyrinth, and the two young girls, Penelope and Helen, who play a major role in his future life.

The Shadow Thieves   by Anne Ursu
After her cousin Zee arrives from England, thirteen-year-old Charlotte and he must set out to save humankind from denizens of the underworld, Nightmares, Death, Pain, and a really nasty guy named Phil.

Runemarks   by Joanne Harris
Maddy Smith, who bears the mysterious mark of a rune on her hand, learns that she is destined to join the gods of Norse mythology and play a role in the fate of the world.

Corydon & the Fall of Atlantis   by  Tobias Druitt
Corydon, an outcast Greek boy with the leg of a goat, reluctantly sets off on another adventure with the "monsters" of Greek mythology when the Minotaur is apparently kidnapped by the people of Atlantis.

Dussie  by Nancy Springer
At age thirteen Dusie makes the horrifying discovery that she, like her New York artist mother, is a Gorgon--a Greek mythological monster sprouting snakes from her head and capable of turning humans into stone with one angry look.

Singer to the Sea God  by Vivien Alcock
When he and his companions flee their island home after the king's court is turned to stone, Phaidon begins to believe in the gods and monsters that his uncle has always scorned.

Voyage of the Snake Lady  by Theresa Tomlinson
After living peacefully for some time following the Trojan War, the Moon Riders, a fierce tribe of women warriors, are driven from their home by Neoptolomus, the avenging son of Achilles, and must fight for their lives to survive storms, shipwreck, and strife.

The Game  by Diana Wynne Jones
Sent to a boisterous family gathering in Ireland by her overly strict grandmother, orphaned Hayley feels out of place until her unruly cousins include her in a special game involving travel through the mythosphere, the place where all the world's stories can be found, and where some secrets of her past are revealed.

Elmhurst Public Library