Kuusen Madoushi Kouhosei no Kyoukan

Years ago, humanity almost got wiped out by huge magical armored insects that had become too strong and aggressive to handle. Because of these giant bugs, humans do not live on the earth anymore, but in floating cities instead. However, this does not mean that everything is lost, because the wizards from prestigious floating wizard academies are fighting these monsters. Kanata Age is a young man now labelled as a traitor even though he was once praised as the "Black Master Swordsman." He gets a chance to repair his reputation by instructing the team E601, which seems to be facing some difficulties. It consists of three girls, Misora Whitale, Lecty Eisenach, and Rico Flamel, each with problems of their own. It appears that Kanata will get in deep waters more than once because of them...(Source: MyAnimeList)