It is unknown when Alex was born, since his movie, A Clockwork Orange, takes place in the not so distant future, but he is young. He was born in England, and caused a great deal of trouble in his youth. He ran around with a gang, and took drugs, not thinking twice about raping a few women. He was eventually thrown in jail for murdering a woman, and accepted a deal years later that if he allowed the government to try a new treatment on him, he'd be out of prison. The treatment consisted of locking his eyes open, and forcing him to watch violent videos with his favorite music, Beethoven, playing in the background. Whenever he thought of violence or sex, he'd get physically ill. Outside of prison, he ran into people he had hurt in the past, and was unable to protect himself. The treatment was decided to be a bad idea, since Alex could no longer make his own choices, so what was the point of being human? The treatment was reversed, and Alex has since gone back to his evil ways(in the American version of the book, and movie.) In all other other of the world, Alex sees one of his old droogs who has given up violence and got married, and decides he should be like him, and stop committing random acts of violence and raise a family.
Alex is the narrator and protagonist of the novel, in which he does not supply his surname. In the film, however, in addition to the surname "DeLarge", we see several newspaper clippings (showing Alex returning to society following his subjection to the Ludovico treatment) where his name is printed as Alex Burgess, in a clear reference to the novel's author, Anthony Burgess.
Alex is portrayed as a sociopath who robs, rapes, and ultimately murders for his own amusement. Intellectually, he knows that this sort of behaviour is wrong, saying that "you can't have a society with everybody behaving in my manner of the night." He professes to be somewhat puzzled by the motivations of those who wish to reform him and others like him, saying that he would never interfere with their desire to be good; it's just that he "goes to the other shop."
He speaks Nadsat, a teenage slang created by author Anthony Burgess. The language is based on English and Russian words, and also borrows from bits of Romany speech, the Bible and schoolboy colloquialisms. He likes milk spiked with various stimulants ("milk plus") or hallucinogens ("synthemesc"). The book goes into much greater detail about the nature of his drug use, describing how the customers at the Korova Milk Bar go away "into the Land." Alex is very fond of classical music, particularly Beethoven, or, as he calls him, "lovely lovely Ludwig Van." While listening to this music, he fantasizes about endless rampages of torture and slaughter to the point of orgasm.