Justice versus Corruption
Batman is primarily concerned with seeing justice done. Working with cops like Lieutenant Gordon and elected officials like Harvey Dent, he wants to restore justice to the corrupted and dangerous city of Gotham. A vigilante, he takes matters into his own hands to ensure the safety of the citizens of Gotham and fight the crime that is threatening to completely overtake the city. He is an agent of justice, symbolizing the goodness and incorruptibility that might be the city's only hope of redemption.
Corruption plays a big part in the crime world of Gotham even before the Joker shows up. The city is controlled by different mobs with competing interests, and unjust dealings are rampant. Thus, it is hugely important to Batman as well as the other leaders in Gotham to try and establish a precedent of justice to replace this fraudulence.
Bearing the Burden
At the end of the film, Batman must decide to take the fall for Harvey Dent's murderous actions as Two-Face. Discussing it with Gordon, they decide that it is best for Gotham if the citizens of the city never know that the noble Harvey Dent was corruptible. In order to keep this secret, Batman says that he will take the fall for Harvey and go on the run from the authorities so that Harvey's reputation is preserved.
In addition to his heroic acts, Batman is heroic because he is willing to sacrifice his own reputation and become a pariah on behalf of the greater good. When he sees an opportunity for the redemption of the entire city, he offers to make the sacrifices necessary to achieve it. Thus, Batman is the ultimate unselfish hero, ready to make sacrifices for his fellow citizens.
Loss of Love
When Rachel Dawes dies, both Bruce Wayne and Harvey Dent lose the woman they love. Bruce has recently expressed his love for Rachel and asked her to be with him, and Harvey has recently proposed. While we the audience knows that Rachel has chosen Harvey, Bruce has no idea, as Alfred never delivers her letter of rejection to him, thinking it better to keep it a secret.
The loss of Rachel is what propels both Harvey and Bruce into their respective solitary lifestyles. After her death, Harvey quickly descends into madness and becomes the villain Two-Face. Likewise, Bruce decides to further disappear into his role as Batman, the Dark Knight. With no promise of a normal romantic and domestic life, he chooses to go full-force towards a life of crime-fighting.
Chaos and Destruction
While Gotham is already quite corrupt and dangerous, the villains that run the street at the beginning of the film are small fries compared to The Joker, who represents a more chaotic and destructive villainy. A showy, unpredictable, and remorseless madman, the Joker's main aim is to make the world as chaotic as possible, to sow the seeds of disruption, anarchy, and mayhem for its own sake. He torches piles of money, blows up hospitals, and paints his face in clownish makeup as part of his horrifying campaign.
In a confrontation with Batman, Joker outlines his philosophy. He suggests that human beings are fine with anything so long as there is a plan. The absence of a plan, he suggests, is what makes people panic."You know what I am? I'm a dog chasing cars. I wouldn't know what to do with one if I caught it! You know, I just...do things," he says. It is this completely arbitrary logic, this sense of randomness and uncertainty, that defines the Joker's character and makes him such a terrifying supervillain.
Human Nature is Essentially Good
Another part of Joker's ideology is his sense that he is simply "ahead of the curve," that everyone is capable of his level of madness and destruction, but just have not been exposed to certain conditions. Thus, he stages various "social experiments" in order to corrupt and destroy human decency. He announces to Gotham that he will blow up a hospital unless someone kills an innocent accountant. He puts explosives on two ferries in the middle of the river and asks the passengers of each to decide whether to blow up the other one.
Joker's plan is faulty, however, as is shown when neither of the two boats elects to destroy the other. As the clock strikes midnight, the villain is confused and seemingly disturbed to note that neither of the boats have exploded. "What were you trying to prove? That deep down, everyone's as ugly as you?! You're alone!" Batman yells at him. In this moment we see that Joker's theory is false; in fact, human nature is more ethical than he imagines.
A Normal Life
Even though Batman ends up being a sacrificial hero, taking the fall in order to save his city, he suffers many crises of faith throughout the film. These crises have to do with his sense that he could put away his Batman identity forever and live a normal life. Particularly when he is reminded of his love for the attorney Rachel Dawes, Bruce wonders if he has found his successor in Harvey Dent. If he can put away his role as a crime-fighter, Bruce knows that he might be able to live a normal life and be with the woman he loves, and this possibility weighs heavily on his mind throughout the film.
Chance
Harvey Dent, once he becomes the villain Two-Face, is defined by his perverse relationship to chance. After seeing his beloved, Rachel Dawes, killed because of Joker's sick game of chance, he becomes bent on deciding the fate of others with the same arbitrary rules. He flips a coin to decide different individuals' fate, and lives his life without principles or logical ethics.
