Birth Of The Firebringer

Description for BIRTH OF THE FIREBRINGER by Meredith Ann Pierce:

Jan, the prince of the unicorns, is high-spirited, reckless-and the despair of his mighty father, Korr. Reluctantly, Korr allows Jan to accompany the other initiate warriors on a pilgrimage. Soon Jan's curiosity leads him, along with his friend Dagg, and their mentor, the female warrior Tek, into the greatest dangers-deadly gryphons, sly pans, wyverns, pards, and renegade unicorns. Yet time after time they are rescued, leading Jan to wonder: Am I the heir to a special destiny?

This is #1 in The Firebringer Trilogy.