Here is a little about the manga:

Crescent Moon is the story of Mahiru Shiraishi, the 'Descendent of the Princess' and her encounters with the 'Lunar Race,' a tribe of demons whose powers are awakened by the moon, strongest at Full and weakest at New.

After Mahiru has a haunting recurring dream, she meets the Lunar Race, which consists of the vampire Nozomu, the werewolf Akira, the fox Misoka, and the tengu Mitsuru. They need her help to recover the 'Drops of the Moon,' the recently-pilfered source of their power.

As the battles to recover the Drops rage on, Mahiru tries to open up the dark, human-hating tengu Mitsuru, and form a bridge between humans and the Lunar Race.