Main campaign background of the role-playing game Traveller, except for Traveller: The New Era,which was set after the fall of the Third Imperium. Classic Traveller is set about the year 1105 after the foundation of the Third Imperium, MegaTraveller from 1116 onward and T4's Milieu:0 in the foundation years. T20, a d20 license Traveller game due by the end of 2002 is set in the year 1000 Imperial.
But first things first: The Third Imperium was founded after the Long Night, a period of decay and dwindling of interstellar contact that followed the Rule of Man (aka the Second Imperium), by Cleon Zhunastu, chairman of Zhunastu Enterprises, a major player in the Sylean Federation. A new calendar is intruduced which sets the Imperial foundation at year 0.
After the foundation, the Imperium (the "Third" is often dropped) quickly expanded in all four major galactic dimensions (Coreward,Rimward,Spinward and Trailing) to encompass about the same space as the Vilani Empire (also known as First Imperium) plus the Domain of Deneb, which includes the Spinward Marches. This expansion was mostly by peaceful adoption of the Imperial Charter by new member worlds, but sometimes had to resort to military might in the so-called Pacification campaigns. The Imperial growth was halted only, when the borders of the Imperium reached their galactic neighbors, the Zhodani and Vargr to Coreward, the K'Kree and Hiver to Trailing and the Aslan to Spinward. Further expansion Rimward was halted due to logistical problems of communication and later trouble with the rebellious Solomani (Earth's humans).
11000 worlds claim membership in the Imperium. The Imperium does not generally impose it's rules on it's member states, each governs itself as it sees fit. The Imperium only governs the Starports on every member world, as well as regulating the traffic between those worlds. Worlds are thus only bound to loyalty to the Imperium, taxes based on their economic productivity and population, anti-piracy legislation and the Imperial Rules of War (Yes, within limits, member worlds could go to war). In effect, the Imperium governs space itself, not worlds. As for citizenship: Any sentient lifeform qualifies for citizenship in the Third Imperium. The Imperial currency is the Imperial Credit, although various worlds also have their own currencies alongsind the Credit.
The Imperium was shattered when Archduke Dulinor shot Emperor Strephon Alkhalikoi and his direct heir dead during an audience in the Imperial Palace on Capital and claimed the Iridium Throne by Right of Assassination, but was forced to retreat to Dlan by loyalist forces. As no clear line of succession offered itself (every claimant had extreme flaws that made supporting him a hard test of conscience), the Imperium fragmented along factional lines and tore itself apart in the second Civil War, which also became known as the Rebellion. The Rebellion ended with no victors as in it's final days an AI computer virus was released that took over or tore down most computer system in known space. Only the Domain of Deneb managed to survive almost intact, protected by it's remote location and galactic position, forming the nucleus for the expansion that became known as The New Era (1200- Imperial).
see also: MegaTraveller, Game Designer`s Workshop, GDW, Imperium Games, Traveller, 4th Edition, Milieu:0.