Disgaea Hour of Darkness is the first game in the series. It is a tactical rpg that was designed and published by Nippon Ichi Software. It was developed and released for the Playstation 2 console in 2003. Although, it has had multiple re-releases, which were retitled to Disgaea: Afternoon of Darkness, for the Playstation Portable in 2007, the Nintendo DS in 2008, and for Microsoft Windows in 2016.
This explanation is very limited and simplified. Some topics werent even covered at all. You can find more info here or check out the GameFAQ page for this game for some really useful walkthroughs.
There are 5 sequels to this game, but they will not be covered in this webpage.