First Contact between the Shavian Empire and the Foible Federation was accidental, when an Imperial Free Trader misjumped 36 parsecs into the Federation and tried to sneak back, jumping into a system with a Federation Navy Base. The news of the existence of another interstellar empire electrified the Federation; scout expeditions were launched into the "no-man's space" between the two, finally making contact with the Empire about a year later.
What resulted was a strategic-level game between Wayne & Don, of which fallout trickled down to affect the player-character groups.
When the Federation scout task force made contact, the Empire's reaction was paranoid; did this new interstellar empire present a threat? Accordingly, the Empire tried to secure the no-mans-space in between as a security/buffer zone -- a space which was already being penetrated & secured by the Federation. New territorial claims and colony sites conflicted, border incidents occurred and escalated, and naval squadrons deployed; eventually the shooting started.
The Empire/Federation War was fought almost entirely in the no-mans-space between the two civilizations, as a limited but escalating naval war between two evenly-matched opponents of completely-different political philosophies and naval doctrines (Imperial "Black-shoe" battleship admirals vs Federation "Brown-shoe" carrier admirals). Civilian casualties were minimal, and no main worlds of either side were touched.
Imperial battleships deployed for their traditional "close-and-hose" tactics, to be overwhelmed by Federation fighters and long-range missile salvoes launching from carrier task forces in a parallel of Yamato's last sortie -- even if they were able to take out the carriers, the fighters and missiles would often chew up the battleships. In return, Imperial battleships proved tough, absorbing many times the damage that would total a Federation carrier. Fed ISBMs and nukes came as a surprise to the Imperials as the situation escalated (the first use of ISBMs -- against an Imperial forward base -- being witnessed by one player-character group). The Imperial Navy rushed to develop fighters (primarily as interceptors to give their battleships some "air cover") and refitted with missiles, sacrificing their ability to run long deep-penetration missions with minimal logistics.
The Federation still held a slight advantage and was pushing back the Imperial claim when the Shavian Throne had had enough; the Imperial Guard Fleet was deployed, and the K-ships began their long, slow voyage from the Imperial Core to the war zone.
As Federation ISBMs and nukes had outclassed the Imperial Navy, so now the K-ships and K-tech weapons outclassed them; the main handicap was that the two large K-ships couldn't be everywhere at once. Fed fighters and missiles chewed up the surface of the K-ships (which could absorb nuke hits through sheer size) in a parallel to Star Wars' attack on the Death Star while K-tech singularity generators tore up Federation carriers from the inside out. Still, the Feds often inflicted enough damage on the K-ships for the Impies to disengage - K-ships were irreplaceable.
However, the K-ships often could stay in combat long enough to get close enough to the system's sun to use their Nova Triggers. Once the Nova Trigger had hit and the sun visibly destabilized, both sides had to disengage and Jump before the sun mega-flared, blasting the planetary system to lava and boiling off the gas giants to where they were useless for refueling. The fact the systems were uninhabited (both sides preferred to conserve habitables and established colonies) prevented wide-scale slaughter. The K-ships, steadily becoming more the worse for wear, triggered novas in system after system, clearing a buffer zone instead of risking themselves unacceptably by penetrating into the Federation.
As casualties and losses mounted, the war became more and more a stalemate; piracy and unrest grew in both the Imperial and Federation peripheries from the drain on the navies, and the costs mounted up. (This was apparently the period of the Brotherhood of the Coast pirate sub-campaign, as Fed forces were pulled from the periphery into the war zone.) Even the invincible K-ships were getting chewed up too much to risk them any further, and the fighting gradually tapered off.
The cease-fire and pullback to original borders ended one hot war and started a cold one, as both Empire and Federation continued to colonize the space between, and intermittent trade began. Imperial Death's Heads and Federation Guardian Knights found themselves in covert ops and counter-ops against each other, the former's superior cyborging and cybertech countering the latter's superior psionics.
This was the strategic situation when both campaigns closed in the summer of 1978, ending our first experience with Traveller.