Alex is an absolute anti-heroic hero of the text. He is addicted only to two things in his life. And they are violence and classical music. By the way, it is hard to realize how a person who likes classical music be a violent one.
Being aggressive he is also a good-hearted and innocent boy. Alex is both horrible and likeable. He commits numerous acts of brutality. He speaks in a slang influenced by Russian, Slavic, Gypsy, Shakespearean English, rhymes, and baby talk, and he addresses the audience directly as “my brothers and only friends.” He loves Beethoven, though the music elicits images of violence and depravity for him.
He also has a gang which consists of Dim, Pete, and Georgie. Those guys are totally crazy, and when they meet each other even trees want to hide somewhere. They are ruining everything they see, touch and hear. Boys are absolute without control, and it is hard to imagine what parent they have to grow up like this.
Alex’s name has three meanings, moreover it is allusions on three important things: the allusion to Alexander the Great (Alex is the gang's leader), the Latinate meaning of "without law" ("A-lex"), and the allusion to Alex's creative use of Nadsat-based slang (a "lexicon" is a dictionary).
The main question in the novel is – is it better to be good by force, or it is better to be evil by choice? We see how Alex’s behavior changes during Part two. He becomes absolutely another boy, with another language, without slang, without all those bad things he did. But, it all looks unnatural. He even loses his struggle to listen to classical music. His goodness is inauthentic, and only in the final chapter of the novel does he outgrow his immature tendencies toward violence and decide to join the world of adulthood.