We are going to use Traveller from 1981 (called Classic Traveller) with some rules from the 1977 version (mostly Referee and setting rules). These are also called the Little Black Books (LBB). I'll also bring in other rules from later versions as needed.
The best source book is the Facsimile Edition which is one book that includes all three Little Black Books and their Errata. The PDF is currently free and the POD book is $9.
For reading, I'd recommend reading:
Book 1: Characters and Combat - read the character half, skim the restBook 2: Starships - skim later on once you're looking at getting a ship/starshipBook 3: Worlds and Adventures - skim the Equipment and Vehicles to know what's available to buy(Obvilously you can read the whole thing too. The Referee advice is more about how to setup the setting so it isn't off-limits)
There are other versions and editions we will NOT be using:
Throws are rolling 2 dice (d6) and trying to hit a number.
6 means get exactly six on two dice.
6+ means get six or higher on two dice.
6- means get six or lower on two dice.
Die Modifiers (DM) are applied to the die roll.
Example. Say being a good Pilot gives a +1 DM, having a co-pilot gives +1 DM but rough weather causes a -3 DM. You need a 7+ to land safely. Rolling a 2 and 3 on the dice gives 2+3+1+1-3=4 so you fail.
Sometimes more or less dice are used, they'll be in front like 1D or 4D.