The Danganronpa series is a pretty hard one to get your head around. First you need to play the two original games, Danganronpa: Trigger Happy Havoc and Danganronpa 2: Goodbye Despair. Then you need to play the spinoff game, Ultra Despair Girls: Danganronpa Another Episode (which is set before the second game but requires you to have played it to make full sense of certain bits of plot). Then you need to watch the above-mentioned anime, except it's split into two arcs: the Future Arc, taking place after the second game, and the Despair Arc, taking place before the first game. And the way you're meant to watch them is Future Arc Episode 1, then Despair Arc Episode 1, then Future Arc Episode 2, etcetera. Confusing.
(There's also a novel, Danganronpa Zero, set before the Despair Arc, which I haven't read. Not even sure if it's officially available in English and my Japanese is still at far too low a level to consider anything beyond a kids' picture book.)
Anyway, the series is excellent if you can get your head round it. Sometimes the gameplay of the two main games can be a bit irritating but the story and characters are well worth sticking with. They're not always an easy watch/play (pick a character as your favourite! They will almost certainly die a horrific, agonising death!) but they're always gripping, always clever, and frequently very, very funny.
And the Despair Arc of the anime has an utterly gorgeous opening sequence. Bear witness. I love it.