The Last Unicorn by Peter S. Beagle
An enchanting, delicate tale. Set in a bewitching fairy tale world.
It opens with a demonstration of the charms of well-told exposition, as he describes the unicorn in her woods, but all is disturbed when two hunters come. They kill nothing, they never even see her, but they talk about how if there ever were any unicorns, they have all vanished. She ponders this and eventually must set out to discover why she is the last unicorn. Whereupon she learns that people no longer see a unicorn when she stands before her -- only a white mare. And a silly butterfly talks about the unicorns and a Red Bull somehow connected to them.
So she wends her way onward, through a delicate fairy tale/ medieval world, where characters have the inklings that they are in a story, and the little anachronism underscore the timelessness of it. She encounters a magician trapped in immortality who resorts, once, to picking pockets when spells fall, a cat who refuses to let one person pet it, a vicious mayor who has outlaws pay him protection money, a carnival with an actual harpy and a spider that really thinks it's Arachne of Greek myth, a foundling prince, a curse with a nasty edge to it, and more.