Roy Mustang
Background
In chapter 58 of the manga (Padding Footsteps of Destruction), Roy is said to have learned his elementary alchemy from Riza Hawkeye's father. In a flashback conversation, Roy is revealed to have become a State Alchemist in order to help the common people, despite the objection of his teacher. Upon hearing Roy's desire for power, his teacher states that he would pass his greatest and most powerful alchemy to Roy under the condition he would use it on the course of good. However, before he could elaborate, Roy's teacher began to choke from coughing up blood and manages only to reveal that he had passed all his secrets on to his daughter, and asked of Roy to look after her. The strange markings on Hawkeye's back is the method chosen by her father to pass these secrets on.
Like fellow State Alchemists, he was sent to completely raze a region Amestris was unable to subdue. It seems that he was 23 at that time (volume 2 and bonus in volume 4). He runs into Maes Hughes and they reminisce briefly about the past and discuss the State's involvement in the War before they are ambushed by an injured Ishbalan. They were saved by a sniper, later revealed to be none other than Riza Hawkeye. Mustang continues through the war with a pessimistic view and considers himself to be a killer, unable to help people as he had previously hoped.
However, Mustang discovers that while he thought he was alone in the war, simply murdering people, he was saving the lives of the men in his unit. This new idea appears to spur him into making an attempt to become the Fuhrer, which he explains to Hughes at the end of the war. He then surrounds himself with people he knows he can trust; Hughes, Fuery, Falman, Havoc, Breda, and lastly Hawkeye. He orders Hawkeye to watch his back, and that if he ever strayed from the path of wanting to help people, of wanting to change the government, it was her role to shoot him.
Personality
Outwardly arrogant and playfully manipulative, Mustang is extremely intelligent and adaptable. These traits usually ensure that he is always one step ahead of his opponents. He also likes to feel in control of the situation. He is one of the superiors of Edward Elric. At the beginning of the series, he appears to be nothing more than a ruthless careerist and a shameless womanizer. However, he is eventually shown to be a rather paternal commander who cares for the emotional and physical well-being of his men. This earns him the fierce loyalty of his friends (Hughes, Hawkeye, Armstrong) and subordinates (Jean Havoc, Vato Falman). He also feels obligated to look out for the Elric Brothers after they become fellow "dogs of the military". This stems from his experience in the Ishbal War where he was forced to kill with his flame alchemy despite learning it to help people. After the war ended, however, his fellow soldiers thanked him for saving their lives. Mustang resolves to protect his subordinates and feels personally responsible for their well being, placing their safety above his own.
He also has a soft spot for dogs, as demonstrated in episode 13 of the anime. However, this is because he saw the dog as the perfect soldier (since it didn't need any pay, didn't fight back and could be treated roughly without complaints). Though a hero of the Ishbal War, he remains haunted by the horrors of war and suffers great remorse for the lives of civilians he took.
Powers & Abillities
A powerful alchemist in his own right, Mustang wears gloves with transmutation circles on them (as seen above) that are made of a material called "pyrotex/ignition cloth" that spark when he snaps his fingers. By adjusting the oxygen densities in the surrounding atmosphere through alchemy, he can create flames anywhere in the surrounding area at will and manipulate them as he desires. While oxygen, by itself, cannot combust, it is assumed that he makes use of the more flammable gases found in the atmosphere such as hydrogen. This assumption is verified in the manga, where it is revealed that it is indeed hydrogen that is burned.
During the Ishbal war, Mustang wore an incomplete Philosopher's Stone on a ring, which increased his flame power and allowed him to destroy entire city blocks in a single blast. He did not have a stone in the manga version of the war, and his alchemy was mainly used for clearing trenches and similar duties.
Mustang is often considered "useless" on rainy days because when his ignition cloth gloves are wet they cannot create sparks. This fact came up at two points in the anime series, first in a humorous moment in the battle against Scar ("The Ishbal Massacre") where Hawkeye tripped her comrade and remarked that he should leave the fighting to others because his alchemy is useless in the rain. Later, when Mustang battles Edward in "The Stray Dog", an anime-only episode, and Ed uses alchemy to get Mustang's gloves wet, Mustang uses Havoc's matches instead.
However, the manga goes into further depth regarding the relationship between Mustang's alchemy and water. His alchemy is actually achieved by using the transmutation circle on his gloves to split water molecules in the air. The energy required to split the molecule is presumably obtained from the murdered souls of Xerxes, as is all Amestrian alchemy. Consequently, Mustang is actually at his most dangerous when the environment is wet, although it is implied that he loses some degree of control as well, due to the fact that all the flames and explosions he creates are large and his own reference to the fact that he was "well-done" when he cauterized his own wounds. In the end, however, Mustang's alchemy is still mostly useless if his gloves are wet and he has no other means of creating a spark, hence Hawkeye's cause for tripping him. The manga has also implied that Roy has knowledge of other alchemy besides the flame alchemy obtained from Hawkeye's back, since he says that her father "[He had] taught me only the basics of alchemy up until now".
Another weakness of Mustang was discovered by King Bradley. During the fight against Mustang, Bradley kept his sword in constant motion, disrupting the air currents in the enclosed space to be in constant flux, hence making it difficult for Mustang to manipulate the air. King Bradley stated, "My Ultimate Eye sees your alchemy at work! Even if you did get off a flame it wouldn't have any accuracy!" Left with no other means of defending himself, Mustang was eventually forced to use it anyway to avoid Bradley's sword strikes and blew an entire wall away, inflicting burns on himself in the process.
In the manga, Roy also carries a gun of unknown make, which he uses against Lust until it runs out of bullets.
