Valdr was an ancient dragon during the Fall whose body was slain by Galbatorix. He lived on in his Eldunarí as one of the one hundred and thirty-six hearts-of-hearts hidden in the Rock of Kuthian. Eragon conversed with Valdr in Inheritance but was confused by the old dragon's tendency to speak using visions and images. Towards the end of Inheritance, when Eragon hoped to raise Brom from the dead, Valdr advised him against it. Valdr's exact age was not known, though he was said to be the oldest dragon among the Eldunarí found by Eragon and Saphira. We can assume that Valdr is a wild dragon because he tended to use visions, images, and thoughts to communicate. In the Ancient Language, Valdr's name meant "ruler".
It is implied that Valdr had discovered molecules (and/or atoms), as he showed to Eragon that "everything that seemed solid was mostly empty space."
Valdr also indirectly contributed to Galbatorix's demise, showing Eragon an image of some nesting starlings whose dreams and worries grew from inconsequential to the importance of kingly notions. This ultimately prompted Eragon to give Galbatorix a profound understanding of what he had wrought in the form of a spell.
Valdr's power was great due to the immense size of his Eldunarí.