Traveller is more than thirty years old – it's been through more publishers than most games have editions. It's had more editions than that and more supplements than you could name on a long afternoon.
That's why every other sentence a Trav GM says is starts 'In my Traveller universe'...
Personally, I run things mostly vanilla at the height of the Third Imperium. Almost none of the setting details are in the Mongoose book – which makes sense since that book is a remake of the '77 original and none of this stuff existed when the game was new. Nevertheless, the following is as close to canon as the game has.
In the time of legend 'The Ancients' had a galaxy spanning civilisation of unrivalled power and knowledge. A true type-III civilization.
Around 300'000 years ago, presumably for reasons that made sense at the time, the ancients plucked up some primitive hominids & canids and scattered them around the galaxy.
The Ancients later had a great big fight and wiped themselves out. These days, a few ruins, some ancient technology, and occasionally, something really cool like a ringworld or dyson sphere survive. Fame, knowledge and riches await the crew to discover some artefact or site of Ancient origin.
The Droyne claim to be the Ancients – or at least, their descendants. Ancient architecture seems built for beings like the Droyne, and no-one knows the Droyne's origin, but the evidence is circumstantial at best.
Hundreds of thousands of years later, the Vilani - one strand of Humaniti - invent a Jump Drive and get out into the galaxy on their own. This was about 4'000 years before the 'present day'. They established the First Imperium, a mighty mercantile commonwealth founded on industry and free enterprise. It ran okay for 2'000 or so years. Then another strand of Humaniti discovered Jump technology. The Solomani, from Terra. The Solomani sphere of influence grew until it encountered the First Imperium, which by that time was starting to rot from within due to gerontocracy, decadence and complacency.
The Solomani eventually came to dominate – a period known as the Interstellar Wars - and the Second Imperium was born. Unfortunately - it was at-best, a stopgap thing. The Second Imperium is today known as the 'Ramshackle Empire'. The Solomani had inherited a dying civilisation and hadn't a clue what to do with over 20'000 worlds all demanding a quick-fix.
The Second Imperium failed. One by one, the space-lanes closed. The ships stopped arriving and each world was left to fend for itself. Galactic civilisation entered the Long Night. The light of learning grew dim, technology was lost and on many worlds the people simply did not survive.
In time, some worlds found each other again, and some clusters of worlds found other clusters. It took a long, long time. What emerged from the Long Night is a feudal Third Imperium with a noble cast directly responsible for the smooth running of some part of the Imperium. Each Noble's livelihood, sometimes life is directly tied to his or her estate, so must ensure that it prospers (so the theory goes).
The Third Imperium governs the stars, but not worlds. Imperial law has (almost) no power over the inhabitants and visitors of a planet, but governs those in space and some ground-based starports, which are legally not part of a planet. Each world is its own sovereign entity, governed as her people see fit and the Imperium seldom interferes.
Seldom. Each galactic sector is ruled by a Duke, who divides his realm amongst the sub sector amongst vassal nobles, who themselves are superior to minor barons and landlords. All of these tiers of nobility, even up to the Emperor himself depend upon the taxes generated by trade and any world so foolish as to threaten that trade shall rapidly find herself facing the armies of the Third Imperium.
Beyond that, misusing weapons of mass destruction, massive abuses of sophont rights and any sign at all of harbouring Psions may provoke the Imperium's wrath. These things generally depend upon the sensitivity and proactiveness of the governing noble, not to mention the size of her army.
The present year is 1105 of the Third Imperium - during the glorious (ahem) reign of His Majesty Strephon Aella Alkhalikoi - 43rd emperor.
