It's an interesting show to think about. Its reputation isn't great and quite a few people seem to think it's boring, but I liked it quite a lot.
Sou Akiyama is a member of the school's feared Astronomy Club. Before you ask, he's the only one who cares about astronomy. The others include Nagisa (manipulative, powerful girl with an influential family), Kenny (an amiably dim but strong American) and Airi (a girl whose hobbies include beating up the entire judo club single-handedly). The last club member is Sou's not-a-sister Kaori, who's lived with him since they were children and is close enough for people to make jokes about them being a married couple.
A bad thing is going to happen, then unhappen. A naked purple-haired girl appears out of nowhere a few days earlier, there are stories of ghosts and suddenly we're watching the same events unfolding again, but differently. Pay attention to those scene-setting date numbers you'll see every so often, by the way.
There are two levels on which this is an interesting show, I think. The first is how the show handles its time travel angle. This is another anime adapation of a visual novel (i.e. computer game) and I'm reminded of another such show, Steins;Gate. Both feel fresh to me in their approach to the genre. They've obviously put much thought into how their time travel rules should work, but at the same time a game is about doing, not philosophising, and there's something practical and down-to-earth about them. The characters' problems are immediate. It's not about asking "do I have the right", but more simply about the universe not doing what you'd want it to and about attempts to fix things just making them worse.
They're both quite slow, mind you, especially in their early episodes. Both are happy to spend quite a long time laying the groundwork and thus require a certain amount of patience from their audiences. Steins;Gate is the better of the two, but they're quite different and I think they're both worth watching.
The other thing that's interesting about this show is how it's handled the problem of its source material. It wasn't just a visual novel, but an adult visual novel. Romance. Porn. Call it what you like. You'd choose one of four heroines and then follow that plot line, having sex with them. The anime, though, is the opposite. The story it's telling isn't about sex, but about romances that, for whatever gentle or well-intentioned reasons, are doomed. Airi has been suppressing her feelings for Sou, because she thinks Kaori has a better claim to him and she knows how Kaori feels. (Watch Airi. She never makes the slightest move on Sou, or behaves anything other than nobly even when she might, perhaps, have stood a chance. You could almost forget that her feelings are there, if you weren't paying attention, but they are.)
A delicate, sombre web is being woven. People fail, or at best succeed in a way that's hard to see simply as a happy ending. Abandoned timelines that we dismissed as "failure, so try again" will still be there. Someone died? Maybe they'll eventually get saved over here, but in that timeline they're still dead. The dominos build up until you can't see any way for a certain character to escape... and she doesn't. Sort of. In the end, there will be reason for hope, but we're left to join the dots for ourselves as the credits roll.
I like the characters. They can be a bit quiet, but there will be emotions under the surface. They're also good friends and they'll go a long way for each other. They're not jealous. They can also be funny. Kenny's English isn't how an actual English-speaker would talk, but that doesn't really matter and he's a lovable lump.
The tech level's a bit higher than is plausible, but then again it had to be for the genre to work. Schoolgirls can create AIs, for instance, and have ten running on a single PC. (I'd need to see their definition of an "AI" to be able to judge that claim properly.) What will happen in the future is even more impressive, but again I'm fine with that.
It doesn't repeat often enough to get boring. It also has clever reasons why one can't just keep going back and trying again for ever.
Is this show a bit arty? Perhaps. Its characters face rejection, failure and the loss of existence and don't turn away. "I can finally move forward now." I think there's a slight question mark over how certain characters are unable to move on in the future and keep on and on at the same devoted task, which perhaps offers a plausibility gap... but that brings us back to "I can finally move forward now". I like Nagisa's backstory in ep.6 and the way it reflects the theme of the future being undecided. This isn't a wacky story. It's quiet, simple and relatively plain, despite the complexities inherent in its premise. I think that's a virtue. I also liked the cast, who made me laugh.
I'd recommend it. Cautiously, though, and not to everyone.