Pathfinder
When Wizards of the Coast announced that D&D 4e wouldn't use the OGL (Open Game License), third party publisher Paizo decided to produce their own version of the world's most popular RPG.
Pathfinder 1e
The original Pathfinder was an updated version of D&D 3.5, nicknamed D&D 3.75. It was intended to be backwards compatible, so that people could continue to use the existing D&D publications with the new game. It also introduced Golarion, the main world of the Pathfinder campaign setting. It proved a hit with players who didn't enjoy the changes made in D&D 4e, and managed to become the top selling RPG a few times before D&D 5e came along.
Pathfinder 2e
In 2019 Paizo published a new edition of Pathfinder. Rather than sticking close to D&D 3.5, this new version simplifies many aspects of game play, aims to provide balanced classes, and promotes creativity and teamwork over optimised character builds. The Golarion setting has moved forward in time, and supplements provide details on various different parts of the setting, notably the Asian inspired continent of Tian Xia, winner of the 2024 Gold ENNIE Award for "Best Setting".
As well as individual modules, Paizo publish campaigns for Pathfinder known as Adventure Paths (APs), which showcase different parts of the Golarion setting. Popular APs include a classic dungeon crawl in The Abomination Vaults, an Afro-fantasy magic school in Strength of Thousands, and Asian horror in Season of Ghosts.
Remaster
In 2023, Wizards of the Coast again began talking about getting rid of the OGL, prompting Paizo to move away from the OGL entirely and start removing or replacing all OGL material from Pathfinder 2e. The resulting Pathfinder 2e Remaster additionally includes the errata from the original printing, and reworks some classes, but remains backwards compatible with the original 2e books. The remastered Pathfinder Player Core won the 2024 Silver ENNIE Award for "Best Rules".
The rules of Pathfinder 2e, both Legacy and Remaster, are all free on the website Archives of Nethys, and the character creation app Pathbuilder is available on the web and the Google play store.