The People's Republic of Coridan is a Federation Member State located in the Alpha Quadrant. (TOS episode: "Journey to Babel", TNG episode: "Sarek", ST reference: Star Charts)
In the 22nd century, the People's Republic of Coridan was one of the leading space powers of known space, possessing the largest known dilithium deposits in the area that later became the Federation core worlds. The Coridanites were rumored to even be capable of reaching speeds as high as Warp 7, though they tightly controlled their exports of such technology.
Coridan Prime was host to a civil war between the Coridanite government, backed by the Confederacy of Vulcan, and various rebel groups aided by the Andorian Empire as part of their on-going conflict with Vulcan. Though the planet had a population of three billion and was quite wealthy, the war left the People's Republic of Coridan politically unstable. (ENT episode: "Shadows of P'Jem", ENT novel: The Good That Men Do)
The People's Republic of Coridan was amongst the various interstellar states that participated in United Earth Prime Minister Nathan Samuels' opening talks for the creation of a Coalition of Planets in late 2154 and early 2155. One of the issues that slowed down the negotiations was a conflict between Coridan and Tellar over trade with the Orion Syndicate. (ENT episodes: "Demons", "Terra Prime")
Unfortunately, Coridan Prime was the victim of a horrific suicide attack by an agent later identified as being of the Romulan Star Empire in early March of 2155. A warping vessel collided with the planet, setting off a global environmental catastrophe that consumed much of the planet's dilithium resources and killed half a billion Coridanites immediately. While the government narrowly survived the attack, as a result of this cataclysm, the People's Republic of Coridan refrained from signing the Coalition Compact that year. (ENT novel: The Good That Men Do)
By 2267, the People's Republic of Coridan had not joined the United Federation of Planets. Its population had significantly decreased, and the maintenance of law and order on its planets was a significant issue. Also at issue was the old question of dilithium trading with the Tellarites and Orions; indeed, things had become so heated that it was feared the Federation was on the verge of civil war. That year, the Federation convened a special meeting of its Member States' ambassadors over the issue of the PRC's petition for Federation Membership. The Babel Conference of 2267 eventually ended in the unmasking of an Orion plot and the decision to allow the People's Republic of Coridan's petition for membership. Vulcan Ambassador Sarek was later regarded as being primarily responsible for the decision. (TOS episode: "Journey to Babel", TNG episode: "Sarek")
The known population of the People's Republic after 2381 is 100 million people. (ST - Destiny novel: Lost Souls)