Revenge
The core of Leonard's existence is his desire to avenge the rape and murder of his wife. Everything he does is in service of enacting revenge on the men who killed his wife. Because he cannot make new memories, Leonard keeps this desire at the front of his mind at all times, determined to find justice, in hopes that it will allow him to move on. His memory-loss condition makes literal how persistent his thoughts of revenge are, in that he wakes up every morning with only one desire—to avenge his wife. The reason Leonard is capable of violence is that he is so bent on revenge.
Trust
Because of his condition, Leonard cannot trust anyone. He can only rely on the facts he has documented—his photographs, as well as the notes that he has on his map and tattooed on his body. As someone who quickly forgets things, Leonard is easy to manipulate, and we see the ways that characters toy with Leonard and take advantage of his lapses in memory for their own personal gain.
By the end of the film, we see that Leonard cannot trust anyone. Teddy believes that he has created a trust with Leonard and he can manipulate him, but Leonard catches on to Teddy's machinations and figures out a way to broadcast to his future self that Teddy is not to be trusted.
Betrayal
Another of the central themes in the film is betrayal. Many people betray Leonard throughout the film, but his primary manipulators are Natalie and Teddy. They use his short-term memory loss to their advantage and prey on him as they know he is weak and has a burning desire to kill his wife's murderer. Teddy uses Leonard to commit murders on his behalf, by leading Leonard to believe that people are his wife's assailant even when they are not. Natalie helps Leonard in certain ways, but also manipulates him in moments of desperation. For instance, she gets Leonard to hit her, and then manipulates him into thinking that her boyfriend did it.
Trauma
The inciting incident that sets the plot of the film into motion is a traumatic one. When we meet Leonard, he is haunted by the memory of his wife's assault and death at the hands of two masked intruders. We see flashes of the incident as if in a horror movie. Christopher Nolan shows the viewer that this incident, in its violence and horror, is a traumatic memory, one that has changed Leonard. Additionally, Leonard's memory condition was brought on by a traumatic head injury. Physical and emotional trauma are intertwined in the film to show the ways that trauma can change people's lives irrevocably.
Memory
The film deals with the theme of memory throughout, as Leonard has a short-term memory loss condition that does not allow him to learn new things. Because he cannot form new memories, he is constantly starting over again—relearning the same facts, making the same mistakes, and re-experiencing the same trauma. While Leonard's memory loss is a literal condition that was brought on by a traumatic brain injury, it is also a metaphor for the experience of being post-traumatic. Leonard is caught in the memory of his own trauma, unable to move forward, frozen in time. Leonard must constantly contend with the fact that he will inevitably lose all the information and memories that he has accumulated since his wife's death and his injury.
Time
Connected to the theme of memory is the theme of time. Time takes on a much more slippery quality for Leonard, because he can never be sure what time it is or what he knows. Thus, he lives outside of time, in a near-constant state of awakening. Director Christopher Nolan simulates the experience of being out-of-step with time in the chronology of the film itself. The main action, shot in color, moves in reverse chronological order, so we see the end at the beginning of the film. Meanwhile, a black-and-white section runs in chronological order.
Identity
Because Leonard cannot remember what has happened in the short term, not only does he lose grasp of how time works, but he also gets out of step with his own identity. Unable to accumulate experiences, he becomes a kind of neutral identity, someone who could be anyone at any moment because he doesn't remember who he was just moments before. At one point, he switches clothes with Jimmy Grantz and takes Jimmy Grantz's car—but later he has no way of knowing that he has done so.