The Foundation is the Firmament’s official ruling government; how true this is in practice depends on how far you are from the core Foundation systems. They can trace their roots back to the original refugees who colonised Tau and brought humanity to the Firmament in the first place. However, the “true” Foundation only controls four star systems: Tau, Amber, Eden and Mira. Centralised control of an interstellar civilisation beyond a few parsecs is simply not feasible with current spike drive technology.
The Incorporated Territories are the individual colonies that joined the Foundation following the Tau Ultimatum of 2830. They are subordinate to the Foundation but autonomous, similar to the relationship between US states and the federal government. Megacorporations thrive outside of the Foundation’s stranglehold, and are often equally powerful as the planetary governments themselves.
Independent Governments are generally found on Rimworlds, though there are a few in the Incorporated Territories that are simply too small to be worth pacifying. Many of them are planetary governments, but some worlds still have individual nation-states or warlords. Some of them outright refuse the authority of the Foundation, but even those that accept it are, practically speaking, impossible for the Foundation to govern or control.
Asimov Incorporated has a primary interest in construction of vehicles and other forms of transportation, including small starships.
Babylon Finance has a primary interest in investments, real estate and PR.
Foundation Express (FoundEx) has a primary interest in interstellar logistics and long-haul freight. They also perform sanctioned salvaging operations and provide private security forces.
FTL Interactive has a primary interest in virtual reality, entertainment and software.
Hornet has a primary interest in law enforcement, particularly police & riot control equipment. They also provide private security forces and security systems.
Icarus Interstellar has a primary interest in starship and spike drive construction. They also specialise in interstellar logistics and freight.
Mjolnir Dynamics has a primary interest in weapons, military equipment and vehicles.
Novacorp has a primary interest in missiles, explosives and other advanced armaments. They also produce laser weaponry and premium firearms.
Pathfinder Networks has a primary interest in communications, exploration & surveillance technologies.
Symposium Syndicate is an alliance of planetary mercantile organisations. They pool their resources to play markets and cooperate for mutual benefit.
Void Industries has a primary interest in mining and resource exploitation.
Xerxes Corporation has a primary interest in weapons, medical research and real estate.
The Anti-Foundation Front (AFF) is strongest on the Rim worlds closest to the Incorporated Territories, though they have members throughout the territories. They formed shortly after the Tau Ultimatum, and are vehemently opposed to the Foundation’s “incompetence, brutality and corruption”. They are strongest on Xanadu in the Hope system, where it is said that Foundation agents actually fear to go.
Viriditas has been described as a loose network of ecoterrorists and anti-corporate subversives, though they would call themselves the only champions of the downtrodden animals and aliens of the Firmament. They operate in disconnected cells throughout the Incorporated Territories, but their primary base is a heavily fortified space station in the Samarkand System. They often get in the way of the cutting-edge genetic research conducted, both legally and otherwise, by the Firmament’s megacorporations.