The Third, Vol. 1

Many years after a devastating war, Earth is now being watched by a group of beings known as The Third, named for the third red eye on their forehead that can access various computer systems. Navigating this barren, apocalyptic landscape is Honoka, a jill-of-all-trades who uses her powers to keep her friends from The Third's deadly grasp. 
The prequel to the action-packed anime takes us to a time before Honoka is known as the formidable but graceful Sword Dancer: to the beginning of her quest to save the world, to a time when she scarcely understands the powers with which she has been blessed...