On his 16th birthday, Tomokazu Mikuri had a realistic dream where he sees a girl battling a giant floating monstrosity. When he wakes up, he is surprised that the girl is actually sleeping next to him... Whenever he sleeps from now on, he ends up back at the dream world, and more and more people that he knows keep showing up there too. He finds out from a mysterious masked woman in the dream world named Silk that they are fighting against one named Faydoom, and he is the one who provides the powers to those girls so that they can fight these monsters. And so it goes... (Source: ANN)

The story is set in the not-so-distant future. Five "Black Points" suddenly appeared around the world as portals to parallel worlds. Immediately after, strange creatures began their invasion from these portals. These creatures are the inhabitants of five worlds—the same worlds in different timeframes. In order to ensure their own future timeframe survives, each of the five invasion forces battle to wipe the other future timeframes out. The key is one card-shaped device. (Source: ANN)

Fourth season of Aggressive Retsuko.

Virtual Reality and the arrival of Circlet Technology has changed people's lives. A new competitive electronic sport called Circlet Bout emerges, and schools duel to determine the strongest Circlet Bout Club and player. One day, Yuuka Sasaki gets mistaken for a challenger and battles against Chikage Fujimura, the best player in Japan, tying the intense fight despite her inexperience. These events lead to her passion for the sport, deciding to become a Circlet Bout player. Two years later, Yuuka moves to Tokyo and enrolls in Union School, a place where she can practice and pursue her dream of fighting Chikage again. After her arrival at the Union School, she discovers the club closed. Now her first goal is to help the athletic Miyuki Kasahara and club manager Ayumu Aizawa reopen Union's Circle Bout Club and return it to its former glory.