Pathfinder is a pen-and-paper role-playing game based off of the d20 System, specifically one used for Dungeons & Dragons 3rd Edition. Pathfinder has since released a second edition, and a later remaster of that edition to distance itself from Dungeons & Dragons after a legal scandal involving the Open Gaming License. The main writer is Jason Bulmahn with publishing done by Paizo Publishing.
All rules for both Pathfinder 1st and 2nd edition can be found for free on the officially supported website Archives of Nethys.