The Nature of Evil
Jack, the protagonist of this story, is undoubtedly an evil person. He has absolutely no sympathy for his victims and tries to justify his behavior repeatedly. This film explores what motivates "evil" people, and instills a sense of fear into the viewer. For example, Jack was actually in a relationship with some of his victims, suggesting that we sometimes don't know a person's true self, even if we are close to them.
The Nature of Art
Throughout this film, Jack is telling the story of his murders to the Roman poet Virgil. The poet takes him through the nine circles of hell, as Jack communicates the gruesome details of his crimes. Disturbingly, Jack tries to suggest his crimes are merely a form of artistic expression.
Storytelling
When Jack is telling Virgil about his crimes, he is ultimately telling his own story. In this story, he doesn't include everything, but instead only includes what he believes are the "highlights." Here, the director is telling us something about the uncertain and untrustworthy nature of a person's story, as it doesn't always include the full truth.