Cortex is the name for the core rules used in the Serenity and BattleStar Galactica RPGs, both products of Margaret Weiss productions (although sadly they no longer supported/licensed). I feel fortunate that I got copies of all three games while they were published. The core rule book is still available, however, both in print and digital form.
So a gamer friend asked of me: "What kind of gaming would I use Cortex for? I play D&D when I want high fantasy, I play Burning Wheel/Empires when I want heavy character pathos and worldbuilding/destroying. Do I use Cortex for combat-heavy games, or social-heavy games?"
And after thinking about it, I answered: Both, but mostly the former (combat and action).
Cortex is a polyhedral system: your character's abilities, skills and Traits are rated in a type of polyhedral die. When performing an action or testing a characters abilities, you roll the relevant dice from your Attribute and one from you Skill. You compare your roll versus another character's roll, or versus a TN set by the GM. Some rolls combine multiple attribute ratings, or you add the attribute values together to determine other thresholds. Cortex also has extended actions (for projects lasting more than a single roll), and a simple chase mechanic. If only it had a social conflict framework. There IS a sort of social meta-game in the generic version of the rules, but it's focuses on legal court battles, which isn't nearly as universal as one could want in a social conflict structure.
Cortex Skills have two tiers: general skills, and specializations within general skills. You can learn general Skills up to a d6 in rating, and beyond that you buy specializations (D8 or better).
Cortex characters also have Traits which are also rated as polyhedrals. Cortex shines in that these advantages can be added to your attribute + skill rolls when relevant, or add flat values to your derived stats. While the core rules have a wide variety of examples, Cortex easily allows for additional Traits to be added for your campaign. Traits can be Assets (which benefit you some way) or Complications (which have a negative cost, but complicate your character's life). The examples in the generic version of the rules have basic examples, but the Traits in the BSG and Serenity books are flavored like the settings they come from.
Cortex has a drama economy, measured in Plot Points. Plot Points can be spent to add dice to a roll, prevent damage, or affect the plot of the story. Plot Points are gained via strong roleplaying.
Combat has one twist that I find interesting. You have track 'stun' and 'lethal' damage separately, on reciprocal tracks against the same value. If you have, say 14 hit points, you're out of combat if you take 14 stun, or 14 lethal, or any combination of stun and lethal that exceeds your 14 total. This is less complicated than, say, the Storyteller damage tracking system, but you can get KO'd real fast in Cortex.
I like how Cortex treats vehicles just like characters: with attributes and skills/specializations and traits. They even have the dual 'stun' versus 'lethal' damage tracking system. 'Stun' to a vehicle meaning non-permanent but disruptive damage.