Overview
Pathfinder is a heroic fantasy roleplaying game system with a high amount of character customization and progression, published by Paizo in 2009. It was developed as a response to Wizards of the Coast transitioning the D&D genre to
D&D 4th Edition 
https://groupfinder.eu/library/dungeons-dragons-4e-2008 , which was seen as a strong deviation from the math-heavy norm from 3.5E. Pathfinder was built using the Open Game License (OGL) to revise and expand upon the beloved 3.5 ruleset.
The system it directly evolved from is
Dungeons & Dragons 3.5 Edition
The second edition of the game was released in 2019 as
Pathfinder 2nd Edition https://groupfinder.eu/library/pathfinder-2nd-edition
Description
Pathfinder 1e is well known for its "
crunch". It relies heavily on strict rules, mechanical variation and math. The system is perfect for players who prefer heavy character optimization and customization, focus on tactical combat encounters and a strong ruleset for almost any situation.
Pathfinder is proud of it's complexity and very much focuses on it. Boasting a massive library of spells, classes, and feats, allows the players to build very mechanically different and unique characters. It is also renowned for its "Adventure Paths": epic, six-part published campaigns that take characters from level 1 to roughly level 20.
System Overview & Key Features
The d20 System & Action Economy
Like 3.5E, the core engine runs on a d20 roll plus modifiers. On every turn the characters have a set structure to perform their actions. Mechanically separated into Standard, Move and Swift actions.
Archetypes & Deep Customization
Instead of relying on complicated "Prestige Classes," Pathfinder 1e popularized "Archetypes." These allow players to swap out base class features for heavily themed alternatives right from level 1. This enables the players an extensive levels of customization when combining with the thousands of available feats to further personalise their unique character concept.
Base Attack Bonus (BAB)
Martial prowess is measured by a Base Attack Bonus. As this number grows, martial classes can eventually achieve "iterative attacks," allowing them to attack with their weapons multiple times per their turns, although penalties apply for repeated attempts.
Combat Maneuver Mechanics (CMB/CMD)
The system introduced two systems to simplify actions like tripping, grappling or disarming your opponents: Combat Maneuver Bonus and Combat Maneuver Defense. This created a single, reliable formula to use when performing maneuvers against an enemy.
Skill Ranks
Instead of a single "Proficiency Bonus" like in modern games, players are given a pool of Skill Points at every level (determined by their class and Intelligence score) to manually distribute across a massive list of skills, allowing for highly granular non-combat abilities.
Lethality and "Crunch"
As characters level up, the numbers grow exponentially. This means, that by reaching higher levels of encounters, characters and their opponents are dealing huge amounts of damage, alongside with various magical buffs and spells that could instantly kill a character. Planning and tracking situational modifiers and buffs becomes vital for survival.
Additional links
pathfinderwiki.com https://pathfinderwiki.com - Pathfinder Wiki
aonprd.com https://aonprd.com - Archives of Nethys (Official free rules database for PF1e)