Founding Titan

The Coordinate (座標) is an ability that is most recognizable for allowing the user to control Titans. It is currently in the possesion of Eren Yeager.

Description
This power is a composition of three different abilities.

First and most noticeable of all, the Coordinate power grants the user the ability to control the Titans at will and make them follow virtually any order. This is seen when Eren unintentionally commanded nearby Titans to eat the Smiling Titan and to attack the Armored Titan. It was also used by the First King to build the Walls, making Titans harden their bodies and confine themselves into the resulting structures. The real limit of this power is unknown, but as it can be observed, it extends to the point of making Titans perform actions that threaten their own lives.

Secondly, the Coordinate allows the user to erase the memory of a single person or even those of entire countries. It was used by Frieda Reiss to remove Historia's memories about her, and by the First King to make humanity forget all the history of the world before the building of the Walls. However, it is known that at least the Ackerman bloodline, the Asian races and the noble families are immune to this mental manipulation, which caused the persecution of the former two at the hands of the monarchy.

Finally, the power allows the user to inherit the lost memories of mankind and those of the previous users, giving them omniscient-like knowledge about the world. Nevertheless, it seems that only the Reiss bloodline can activate this ability from the beginning, since Uri and Frieda Reiss showed signs of being aware of that knowledge immediately after obtaining the Coordinate, while Eren has just unlocked some vague memories after years of having received it.

The overwhelming extent of these combined abilities makes the Coordinate to be referred to as the "invincible power", and the user to be called "God", as stated by Rod Reiss.

Even so, it is noteworthy that, despite the fact that all of the Coordinate users could use this power to easily wipe out all Titans and free humanity from their struggle if they wanted, and despite all the wielders have expressed the desire to do that before obtaining the ability; once they receive the memories of the events that led to the invasion more than 100 years ago, all of them have finally decided to do nothing, and not even want to reveal the reason to anyone, showing a silent concern and culprit for the knowledge received. Frieda Reiss used to suffer from fits of madness and depression due to those memories, and claimed that humans were sinners who deserved their punishment.

The Coordinate is apparently not inherited by bloodline, and the only way to get it is by eating the previous user. This is usually done by using a serum to transform into a Titan, then eating the holder and thus regaining human form, plus obtaining the Coordinate power. This means that all the Coordinate users have been also Titan Shifters.

The Coordinate originally belonged to the Reiss royal family, which passed it down generation to generation through the previously described process. However, seeing that they would never do something to stop the Titans despite having the capability, which allowed the invasion of Shinganshina and the death of his wife, Grisha Yeager stole the Coordinate by attacking the Reiss family in his Titan form and eating the former wielder, Frieda. He then transformed his son Eren into a Titan and allowed himself to be eaten by him, so that he could master the Coordinate without the memories and influence of the Reiss bloodline and accomplish the goal they never did.

Trivia

 * The Coordinate, as well as other Titan abilities, is retained in the user's spinal cord, so it is not necessary to actually eat the whole wielder to obtain or transfer the power.
 * According to Rod, this power can only be used to its full potential by a descendant of the Reiss family. That is why Rod tried to have Historia eat Eren, due to the fact that she was the only remaining heir of the Reiss bloodline.
 * It is currently unknown why the Ackermans, the Asian groups and the noble families are the only people unaffected by the Coordinate's memory-erasing power.