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From MangaHelpers:

This manga is related to the anime, "Rinne no Lagrange", although it has a different storyline.

On the planet of De Metorio, Izo is a student in the royal pilot training facility, together with his few classmates, Kirius, Arei, and Sanu. One day, they get a new student teacher who happens to be De Metorio royalty, Princess Yurikano. She runs things a lot differently than Izo and the others are used to, but there's more to this princess than meets the eye. Will Yurikano be able to get Izo and the others to accept her training, and will she be able to survive the enemies that are gathering against her? [tethysdust]

Kisaragi Saya is a happy, small-town schoolgirl who spends peaceful days with her friends. She mostly hangs out with her friend Yuka, the twins Nono and Nene, and the class rep, who seems to have a crush on her. Saya is also intrigued with a mysterious loner named Tokizane, who always comes to school late. She lives at home with her widowed father, and often eats at the neighboring cafe 'Guimauve,' which is run by the excellent chef and family friend Fumito. Her life may seem very tranquil and happy from the outside, but Saya also secretly wields a mystical sword to defend the town from the 'Old Ones,' monsters who eat people. Lately, Saya is beginning to think that there's a lot more to the situation with the Old Ones than she knows...