The official website and Twitter account for Dr. STONE confirmed the second season, Stone Wars, for January 2021. A new preview trailer was released.
The anime adaptation is based on the popular Shonen Jump manga written by Riichirou Inagaki and art by BOICHI. TMS Entertainment was in charge of the animation producton for season 1, which originally premiered in July 2019.
Crunchyroll describes the show as:
Several thousand years after a mysterious phenomenon that turns all of humanity to stone, the extraordinarily intelligent, science-driven boy, Senku Ishigami, awakens. Facing a world of stone and the total collapse of civilization, Senku makes up his mind to use science to rebuild the world. Starting with his super strong childhood friend Taiju Oki, who awakened at the same time, they will begin to rebuild civilization from nothing… Depicting two million years of scientific history from the Stone Age to present day, the unprecedented crafting adventure story is about to begin!
Source: Dr. STONE official Twitter