If you haven't yet come across the Danganronpa series and would like to get into it, stay away from this manga at all costs.
The Danganronpa games are very long and and detailed in the characterisations of characters and the mystery's themselves. Trigger Happy Havoc itself takes around 20 hours to complete. It also received a rather rushed version of the story which only had 12 episodes. This manga adapts the anime in only 4 volumes so you'd expect this to be even more rushed, and that's exactly what we got.
The characters receive very little development when compared to the games and even the anime.
The murder reveals are also very lacklustre and anti-climactic. Class trials are also very quickly done with very little build up or suspense to revelations. I am only 2 volumes (8 chapters) deep and the third murder has already taken place, that's how fast paced this manga goes.
That being said, I don't think this manga was intended as the introductory piece for newcomers at all and shouldn't be treated as such. In fact, this should be more geared towards established fans of the series looking to own more Danganronpa related media. The fantastic art is also a plus.
So to conclude, should you read/buy this? If you haven't tread foot into the Danganronpa series yet, then stay away. Watch the anime or ideally play the games. If you are a big fan of the series already then you could consider getting these. The covers look and feel great and more Danganronpa never hurts.