No date announced yet for the premiere of season 2. The announcement comes after the finale of season 1 just aired today. See the Crunchyroll article for more information. Season 1 synopsis from AniList:

They say whatever doesn’t kill you makes you stronger, but that’s not the case for the world’s weakest hunter Sung Jinwoo. After being brutally slaughtered by monsters in a high-ranking dungeon, Jinwoo came back with the System, a program only he could see, that’s leveling him up in every way. Now, he’s inspired to discover the secrets behind his powers and the dungeon that spawned them.