15 years ago, the world discovered magic as well as mythical beings (basically beings from various legends) in another dimension. Humankind learned to summon these dangerous mythical beings and use their power to great effect. 7 countries' formed contracts with these "Gods" and gained their intelligence as a result. Gods will chose their summoners on their 14th birthday and give them a Stigma. Schools have been set up to train Summoners and Magical Swordsmans (basically bodyguards that give the summoners time to cast their spell) as a result.
15 years laters after the finding of magic, Hayashizaki Kazuki is chosen as a Summoner and given a Stigma to indicate that. This is surprising since males aren't chosen as Summoners due to their low amount of mana compared to females. As the first male to be a Summoner, Kazuki, is under a lot of scrutiny by almost everyone.
To complicate matters his sister (who's a Magical Swordsman) is against him going into Summoner school to train there as a Summoner. Because Summoners and Magical Swordsman have a cat-mouse thing going on where Summoners look down on Magical Swordsman as inferior so his sister naturally is against him going there. She'll stop him even if it means going to war.
Kazuki, however, is determined to thrive in Summoner school and have already determined to give it his all. Even if he's the lowest ranked student (ranked E) and his fellow students intend to demean him he'll prove himself as the strongest Summoner.
Otanashi Kaguya (音無輝夜) is the student council president of the Magic Division. She is also the strongest Magika student in the academy and one of the main heroines of the series.