Percy Jackson and the Titan's Curse (Book 3) by Rick Riordan

Half Boy. Half God. All Hero. It's not every day you find yourself in combat with a half-lion, half-human. But when you're the son of a Greek God, it happens. And now my friend Annabeth is missing, a Goddess is in chains and only five half-blood heroes can join the quest to defeat the doomsday monster. Oh and guess what.