The Last Unicorn - Peter S. Beagle

The unicorn lived in a lilac wood, and she lived all alone. So she ventured out from the safety of the enchanted forest on a quest for others of her kind. Joined along the way by the bumbling magician Schmendrick and the indomitable Molly Grue, the unicorn learns all about the joys and sorrows of life and love before meeting her destiny in the castle of a despondent monarch and confronting the creature that would drive her kind to extinction.