Kagi Hime Monogatari: Eikyuu Alice Rondo

Average high school student Aruto Kirihara is obsessed with the Alice stories, written in this alternate world by the enigmatic recluse, Alternite L. Tachyon. One night, while writing his own version of a potential "third book," he sees a girl flying in front of a full moon... and she looks just like the "Alice" in his imagination. Aruto runs out of his house and chases the flying figure from the ground, ending up at a library, where he witnesses her in combat with another costumed girl. And so begins his sudden introduction to the world of Alices, an elite club of super-powered teenage girls who regularly fight in an extra-dimensional Wonderland in order to steal each other's "hidden stories." When all of the stories have been gathered, they will form the legendary third volume, "Eternal Alice," and the possessor will be granted one wish. It probably won't be Aruto, who can't turn into a magical girl. But it could be his doting little sister, Kiraha. Or maybe the girl of his dreams, Arisu... (Source: Discotek Media)Generally, it is believed that Lewis Carroll wrote two books about Alice. However there is another Alice book, "Endless Alice". Somehow, the pages of the books were taken apart and they are lying in girls' minds.