Hi Hopeless
This may ramble a bit...
Traveller 2300, or Mongoose 2300AD, is a hard science fiction roleplaying game set in the year 2300. It changes several of the basic assumptions from the core Traveller rulebook, most notably the classic J1, J2 etc. jump drive is replaced with a stutterwarp and Grav tech does not exist.
A stutterwarp drive operates by moving the starship instantaneously from one position to another without passing through the intervening space. This jump is only a few hundred meters long, so to achieve superluminal travel, the drive is cycled thousands of times a second, performing many short hops - stuttering. The drive system has an inherent limitation that it builds up a "charge" that must be discharged in a gravity well of 0.1G or greater, but the drive efficiency drops as the local gravity increases. If the drive is not discharged before the ship travels 7.7 light years, the drive destroys it self in an energetic release of hard radiation, that will kill the crew and ruin the drive (and your day).
Since there is no grav tech, there are no CG or grav plates, so artificial gravity is generated by using rotating sections on craft.
The background is an extrapolation of the Twilight 2000 timeline, although the details of the Twilight period are not well documented. Humanity has colonised space to a radius of about 50 Ly, and has met several alien species. Humanity remains balkanised, with France, Germany, UK, America and Manchuria being the main colonial powers, although Mexico, Azania, Japan, Australia and several other nations have outposts or colonies.
The star map is based on what was, at the time, the most accurate list of stars within 50 ly of Earth, the Gliese Catalogue of Nearby Stars 1969. Unfortunately we now know that several of the stars in the catalogue have wildly incorrect information so it's no longer the most accurate game map out there, but the map created from the catalogue is internally consistent, and is still used.
This places 2300AD, along with the potential divergence from our history with Twilight, into effectively an alternate universe, with stars in slightly different places, and the new dark age of Twilight starting.... about now.
The overall tech level is 10-12, with 10 being old commercial, 11 being new commercial and 12 being new military (cutting edge), although some tech is more advanced than the baseline Traveller.
Character Creation is broadly the same as the Core Book, but with several additions. Traits can be gained during character creation that are modifiers or descriptors, sort of like perks and flaws, but related directly to character choices, so a brawny character who is a Mesomorph body type will have traits that give advantages to checks relating to strength, but may be disadvantaged relating to dexterity. Other traits, such as enemy or fame or even wealth, are picked up as background life events.
There are a couple of extra careers that are translations of the old GDW careers, and some modifications to existing careers.
The background to 2300AD means that characters are much less likely to have their own ship. It's not impossible, but the crewing requirements for ships are much higher, typically 12-15 people for the smallest of vessels. Ships are also very expensive, so tend to be owned by nations or corporations (although there is a strong body of fan material that shows the costs are far too LOW when you consider the profits to be made from shipping cargo).
Published adventures in the past have tended to fall into one of three camps - The war against a race of belligerent aliens called Kaefers, exploration and survival on unexplored worlds, cyberpunk adventures in the high-tech core worlds (a late and rather tacked-on trope for the original 2300AD). The Kaefer war came to dominated the original line, with only a few published adventures not featuring the grumpy lobster faced antagonists in some way. I'm pleased to say that the new, original material published for M2300AD has been of the second category, exploration and survival.
I disliked the combat mechanics in the original version, and the system of skills and checks is more or less the same between the two versions. The skill list for the Mongoose version is slightly more compact, but I have just converted 30 odd NPC from one version to the other, and there wasn't one I couldn't easily switch over.
I'm a big fan of 2300AD in all its forms (I bought the first run of the original Traveller:2300AD the week it was available in the UK) and I think the new Mongoose version is the best version so far. If you are looking for a sfrpg with a hard science basis I recommend it.