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In case you're still interested in the game, I ended up typing up this summary for you since a lot of stuff is scattered throughout the wiki.


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So starting off with the two most important things, pilots and titans. Pilots are, of course, people who pilot the titans, and there are numerous 'gradings' and certifications of titans, most of them for civilian use since that's what titans were originally designed for. The hardest certification to receive is the combat certification, which involves a lot of physical and mental tests and exams, and mean that you're fit, smart, and capable of using things like jump jets and piloting a titan as if it was an extension of your body. Pilots get this way through a combination of hard training and augmentation, more training for the Militia who lack a lot of more sophisticated things without stealing them, and more augmentation for the IMC who can quickly churn out more pilots to match their massive industrial war machine.

Titans, as stated before, are mechs originally designed for civilian use and originally designed by the IMC, and have since been introduced to warfare as they are extremely dexterous for several hundred tons of hulking metal, and capable of putting out firepower equivalent to that of main battle tanks. Titans are designed in a bipedal form to also act as an extension of a pilot's body, and likely require extreme amounts of spatial awareness and dexterity in order to be piloted effectively in combat (which also lends to a pilot's maneuverability and ability to use jump jets). By and large, titans only have basic AI with canned personalities called a Titan OS, and are really only capable of limited individual movement and combat ability. This is prevalent through first generation titans (the Atlas, Styder, and Ogre) which were civilian titans quickly repurposed for war, up to second generation titans (more specialized and less flexible than first generation titans, but much more suited to fighting). Third generation titans, of which there currently only exists the Militia-designed Vanguard, take it a step further by giving the titan a truly intelligent AI, and forming a neural link to its pilot. This means that pilot and titan are bonded on a whole different level, which makes them both much more effective when fighting together, but also means that you can't simply swap between titans on the fly. Any experienced Vanguard pilot can mop the floor with entire squadrons of 2nd or 1st generation titans, but are also much more costly and only issued to Militia special forces, (the SRS). [/hider]

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Onto a brief timeline:
The IMC (Interstellar Mining Corporation) which dominates the Core Systems was involved in a series of wars called the Core Systems Conflicts, and after the wars were over, basically funded a bunch of colonization efforts out into an area of space called the Frontier, giving land and money to a lot of the soldiers who had fought for them as recompense for their service. The Frontier is a massive stretch of extremely habitable planets full of life and alien ruins, but was at the time an extremely long distance from the Core Systems, requiring years upon years of travel, likely decades at its most distant points. The IMC would fund these colonization efforts for a while, before their interest dried up due to the distances involved, and turned inwards to recover from the wars they'd fought.

This meant the Frontier was left to develop on its own for a very long time, developing its own culture and civilization independent from that of the IMC, as well as being a place of great lawlessness. The Wild West in space. With the advent of the Jump Drive, however, a much more effective form of FTL, the Frontier quickly became much closer, and the IMC regained interest in its vast and largely untapped natural resources in order to feed increasing demand in the Core Systems, which had long been depleted of such vast reserves. Claiming that since they had originally funded colonization efforts into the Frontier, the IMC claims the majority of the Frontier as their own, and quickly moved in with their forces to boot off colonists and set up mining and production centers. Tensions rise between the Frontier and the IMC, slowly escalating into armed conflict called the Titan Wars (likely because this was where titans were first introduced into warfare). The Frontier organizes into a ramshackle military called the Militia made up of farmers with guns, pirates, and outlaws, in order to combat the IMC. Due to the Militia's lack of organization and the IMC's willingness to use cutthroat tactics and massive logistics and supply advantage, as well as likely being the ones to first introduce titan warfare, the war ends in an IMC victory, although the Militia continues to wage guerrilla operations throughout the Frontier.

Over fifteen years pass before the Militia begins an offensive that starts what is called the Frontier War. The Militia's offensive ultimately culminates in an attack on Demeter, the IMC's "half-way point" between the Core Systems and the Frontier, a refueling station for ships making the long jump from there to here. It would cut off the Core Systems from the Frontier, and leave IMC reinforcements years away from coming into the Frontier. This is the 2nd to last mission in the first Titanfall story, and is basically the ultimate victory for the Militia over the IMC during that game. The IMC splinters somewhat, forming the Remnant Fleet, led by an AI called Spyglass that was essentially in charge of operations in the systems, which remains an obscure threat that hits not only Militia aligned targets, but also IMC facilities, and the Remnant Fleet has largely since been declared rogue by the IMC.

Roughly five years later, the IMC is finally capable of reinforcing the Frontier once more, which sparks the Frontier War off in earnest again, with the Militia having since reorganized into a much more professional military, though still by and large united only by their combined dislike of the IMC, and having designed their third generation Vanguard titan. The campaign of Titanfall 2 plays out, which really doesn't have all that much impact on the war, other than the main character stopping a super weapon, but otherwise the war remains.
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Hope this helps, and I can provide any further information if you need it.