The Last Unicorn by Peter S. Beagle
She lived in a Lilac wood all alone and she was very old, she believes she is the last unicorn in the world and sets off to meet a magician (whose magic does not always work!). On her way she comes across a King Haggard who had banished Unicorns from the land. A lovely story of fantasy.. or is it ? Litrasaurus is not so sure!