Personality:

Quatre's personality changes and grows throughout the series. At the start of Episode Zero, we see a boy who feels like a pawn who's lower than dirt, an utterly useless tool who's only good for one purpose: to be a loyal heir who would one day inherit the family business. He is extremely resentful of his father and is seen by his chaperons as nothing more than a rich brat. Despite this, Iria mentions that Quatre is a gentle child, suggesting that, perhaps, the boy we see is not the real Quatre but a Quatre who is emotionally wasting away.

We begin to see what he's truly capable of when Rashid knocks some sense in him. He's smart, strong, and an excellent strategist, and he wants nothing more than to be useful and find his place in the world. When he parts with the Maganacs for the first time, he tells them that he will come find them and that he won't go to Earth to run away but to find himself.

When the series begins, two years have passed, and we see a much kinder Quatre. He's gentle, selfless, trusting, and seemingly eager to make friends. Rashid warns him that, perhaps, he may be a bit too trusting, but as mentioned in the history section, he possesses some type of extrasensory ability that allows him to read people a bit easier than the average person. He proves to have good judgment when choosing whom he allies himself with.

We're treated to a few other aspects of his personality when he meets with his father on the resource colony. Obviously, they still don't see eye to eye, and Quatre doesn't hold back when they disagree on his role in Operation Meteor. It could be said that he's a bit of a rebel, one who's determined and fights for what he believes in.

Because of his gentle nature, the death of his father hit him hard, and with the combined stresses of being betrayed by the colonies and becoming separated from his friends, he snapped. Wanting revenge, he built Wing Zero, his outrage and injustice becoming the perfect tools for the mind-altering effects of the ZERO System. When Trowa finally snaps him out of it, he returns to his kind self, but we later learn that he'd wanted to rebel against it. He hated his kindness, which only served as more fuel for his actions while under the influence of ZERO.

By the time the series ends, he's a much more well-adjusted person. He's found his place as the strategic leader among the Gundam pilots, finally confident in the usefulness of his abilities.

Other: Quatre is an accomplished musician! He plays the violin and piano (and possibly more) and uses music as a means of relaxing.
Additional Links: Quatre's article on Gundam Wiki!