Violence and instances of criminality are ubiquitous in this book. In just a few chapters, Alex and his entourage have performed every trick in the criminal's Bible: boozing, doing drugs, mugging, robbing, gang fighting, grand theft auto, gang rape, reckless driving, vandalism, arson, and murder. What is more, there's also plenty of discussion of probation officers, juvenile delinquents, prison life, police brutality, and even a forced suicide.
Alex commits crimes for the sheer joy of it; Dim is too dim to be thoughtful about his motivations; and Georgie commits crimes for monetary gain. Thus, Alex and Georgie are your typical criminals, while Dim is a mere victim of his circumstances.
In his vivid descriptions of brutality in the work, Burgess uses violence not only to contrast the forces of good and evil, but also to cause readers to look within themselves at their own capacities for nastiness. Thus, the depictions of violence are indispensable to A Clockwork Orange.