In the anime series, the members of Six Gravity and Procellarum are all living in the same dorm building. Hajime Mutsuki and Haru Yayoi, the oldest members of Six Gravity, are first year university students. Each episode of the series will feature a different main character. (Source: MAL News)

The third season doesn`t have a particular story behind everything (like "Valkyrie Ghost" in the second season). It just tells 6 stories about the life of Kazuto & Co. with some additions: Raine and Chorus get a house on earth, the last three Valhalla princesses each get an episode, and in the last episode Kazuto and Valkyrie, who in the same episode managed to stay adult, >try< to marry again. (Source: ANN)

The strange and magical events of the last season have left Kazuto with two Valkyries. He now finds himself living with and looking after both a teenaged-princess Valkyrie, as well as the child-princess Valkyrie! And they still have not yet gotten married... (Source: AniDB)

The story is set in the 15th century, during the Hundred Years' War between France and England over the succession to the French throne. Montmorency, the son of a noble, immerses himself in the studies of magic and alchemy at a royal knight training school. However, following France's crushing defeat at Agincourt, the school is dissolved. Having lost everything and now a wanted man, Montmorency, who had just become an alchemist, encounters a mysterious village girl named Jehanne. (Source: MAL News)