Arioch,
The Avalanche game Imperium is a remake/update of the ancient GDW game Imperium, a game whose first version predated Traveller itself.
In the first version, the Imperium of the title is comprised of seventy stars and centered on Capella. In GDW's later releases of the game, that pre-Traveller Imperium becomes the Vilani Ziru Sirka.
With the exception of a few minor rules and some descriptive text, the various GDW releases are the same. The Avalanche version has a lot of 'chrome' compared to the GDW versions; much better counter graphics, fancier map, better tables, and many, many new rules. These rules IMHO add nothing substantial to game play and add quite a bit to game time. One new wrinkle, a tactical movement setup, provides so little benefit that players generally ignore it.
I was a wargamer well before I was a roleplayer. I am still more of a wargamer than a roleplayer. I even play Avalon Hill's Fleet series with all the advanced and optional rules. IMHO the chrome Avalanche added to Imperium is not worth the effort.
Imperium begat a GDW spin-off titled Dark Nebula. Set during the Long Night, it modeled the Aslan-Human wars of that period in Dark Nebula sector. With the exception of a few rules, one of which changes the map each time the game is played, the two games are essentially similar.
Both games use the usual Ugo-Igo turn structure. Players determine how many resource points the systems that they own provide. They then spend those points to buy military forces like ships, troops, and planetary defenses. Which kinds of ships and troops are available for purchase are constrained by various rules; the Vilani side can't build certain vessels without permission from the Emperor, the Terran can't build ship B until ship type A is destroyed, neither can build more ships/troops than the counter mix provides, etc. Maintenance fees also must be paid.
Movement is along 'jump lines' between star systems. Notes in the first version reveal this idea came from Pournelle and Niven's Mote in God's Eye(1). (In Dark Nebula a research advance allows movement off the lines.) The phasing player; whose turn it is, has unlimited movement, he can move his ships and stacks as far and as long as he wants. The non-phasing player is then allowed to move a designated reaction force three times.
Combat occurs when ships occupy the same system or when troops are landed on planets that have opposing troops/planetary defenses. Combat itself is straightforward, you line up the opposing ships/troops and roll against various attack factors on a combat results table. Ships can be damaged or destroyed. (The tactical movement setup I mentioned in the Avalanche version comes into play here and provides so little benefit that players generally ignore it.)
One nice feature of the games is that they present a series of wars and not just one war. There are rules for the periods of peace inbetween each war. Territories get adjusted in certain ways and armed forces drawn down before the next war kicks off.
IIRC, Avalanche Press made Imperium part of a recent 'Fire Sale'. They dropped prices to move certain titles out of their warehouse. After the sale, all unsold copies of the titles in question were to be burned. Make of that what you will.
Have fun,
Bill
1 - You can see that the 'jump lines' in Imperium and Dark Nebula have a non-Traveller lineage. You can also see how jump lines, and the way movement is handled as a whole, were chosen as a way to speed game play. Sadly, the authors of GT:ISW failed to appreciate that and the playtesters, of which I was one, failed to explain that to them. Subsequently, GT:ISW chose to 'explain' the presence of jump lines in a decidely canon breaking matter, further differentiating GT from the rest of Traveller.
It was as if the authors chose to 'explain' why Imperial, Sword World, Vargr, and Zhodani fleets in the Fifth Frontier War boardgame seemingly don't have jump fuel regulators. They mistakenly confused an aspect meant to streamline play in a boardgame with an actual aspect of the overall game setting.