In -3224 (earth year 2092) humanity reached the stars only to find... humans. For hundreds of parsecs to the galactic core there was a multitude of worlds inhabited by humans. There were alien races and alien ecologies but humanity dominated. These worlds were united under the rule of the Vilani in the Ziru Sirka. This translates to the Grand Imperium of the Stars. By the time humans from Terra made contact the Ziru Sirka was over 1,500 years old.
However this 1,500-year-old rule had a price in cultural rigidity and stagnation. The dynamic Terrans exploited this in a series of interstellar wars that brought down the Ziru Sirka. In its place the Terrans erected the Rule of Man uniting Vilani and Terrans under a single rule. But the dynamism of the Terrans (now known as Solomani) could not arrest the decline of Vilani culture. Within 400 years; civil wars and economic upheavals caused the collapse of the Rule of Man. With the collapse, both Vilani and Solomani worlds slide into the 1,500 year Long Night.
After 1,500 years the Long Night was beginning to recede and many worlds started reaching out to the stars again. On the world of Sylea a man named Cleon Zhunastu had a dream of restoring the glory of the Ziru Sirka and the Rule of Man. In a thirtyyear campaign he transformed the Sylean Federation into the basis for the Third Imperium. In the 654th year of the Sylean Federation; Cleon and the Grand Senate of the Federation proclaimed the Third Imperium with Cleon Zhunastu as Emperor Cleon the first.
The Third Imperium:
Founded One Thousand One Hundred and Five years ago by the Emperor Cleon I, the Third Imperium has expanded to encompass over 11,000 worlds. The Emperor Strephon currently rules the Third Imperium. The Emperor has appointed nobles to aid his rule of the Imperium. Dukes, Counts, Barons, and Knight go forth among the worlds of the Imperium to bring the Emperor's words and enforce the Emperor's law. The Imperium is not an oppressive empire crushing all dissent before it. It is a grand confederation to provide for the common defense of its member worlds; to ensure that commerce and trade flows freely among the stars. Other than regulating trade and providing military forces the Imperium does little to interfere withthe internal affairs of its members.
The Human Question
Throughout all of history one question remained; from where did humanity come from? Who placed us among the stars?And why did they do this? As the years of Third Imperium rolled on, archeologists found out several things: first genetic analysis indicates that humanity was scattered around 300,000 years ago. Second there are many sites around the Imperium on the various human homeworlds and other world that were built by a non-human race over 300,000 years ago. Third that in a 10,000 year long war this race destroyed itself in leaving humanity to fend for itself. Last the best candidate for the original human homeworld is Terra the homeworld of the Solomani. The race that scattered humanity was dubbed the Ancients. In addition to humanity it is believed that ancients took members of the canis (dogs, wolves, etc) genus and uplifted them to sentience as the Vargr.
No one knows why the Ancients choose humanity to scatter among the stars. There are no answers for the reason why the ancients destroyed themselves in a great war. These questions remain and more are needed to be answered.
Aliens
In addition to the scattered descendents of humanity, alien races are found throughout the stars. There are two traditional categories that alien races have fallen into. Major races that have discovered the jump drive on their own and minor races that have learned the secret of the jump drive from another race. The major race includes Humanity, the Aslan, the Vargr, the Hiver, the K'Kree, and the Droyne. The Ancients placed humanity on many worlds. Only three of them discovered Jump Drive on their own; Solomani of Terra, Vilani of Vland, and the Zhodani of Zhdant.
Influences and inspiration
Marc Miller lists a number of books that influenced Traveller and provided its key features:
Dorsai, Gordon R. Dickson, 1960
Dumarest of Terra saga, Edwin Charles Tubb, 1967-2008
Envoy to New Worlds, Keith Laumer, 1963
Hammer's Slammers, David Drake, 1979
Retief's Peace, Keith Laumer, William H. Keith, 2005
Space Viking, H. Beam Piper, 1963
The Cosmic Computer, H. Beam Piper, 1963
Design assumptions
Since the earliest rules for Traveller, the game has emphasized five significant points:
I. Travel. Travellers travel within the limits of jumpspace, high fuel usage (...includes wilderness refueling), and gravitics. The Jump Drive (100+ tons, one week's time) is the key to interstellar communication and travel.
II. Open Limits. Rules and options set open limits, allowing many possible worlds, characters, aliens, ships, beasts, tech. It is a DIVERSE space, including anachronism and atavism—the rules present tool kits and systems for designing your universe or expanding on the existing ones.
III. Material. The universe is cosmopolitan, understandable, and consistent. There is high-tech, atavism, and anachronism (shotguns & cutlasses) that defies SF conventions. Conventions of the current world are followed and expanded as needed to reflect the future settings.
IV. Agency. Self-Reliance. The remoteness of authority, speed of jump, starports as "deep water" ports, explicit feudalism (...and even piracy) supports, empowers and requires the players to make their own decisions and act. Actions have consequences, and combat is deadly, so activities require forethought.
V. Sociology. Interstellar society is socially stratified (high, mid, and low passage; SOC), but people are still human. The typical game shows how being a traveller crosses classes and breaks stratification. Patrons mediate between the setting and players' goals via Push, Pull, Enigma, and Gimmicks.
Any questions and traveller wiki has you covered.