Mistaken Identity
Mistaken identity is one of the film's main themes, and the main reason the Dude gets caught up in this mess in the first place. He is mistaken for the other Jeffrey Lebowski, whose wife owes money to a porn magnate. Because of this, the Dude takes the brunt of a beating intended for Lebowski. While this seems like a one-time incident, the instance of mistaken identity changes the course of his life in enormous ways, and he becomes embroiled in a convoluted plot all centered around the other Lebowski's life. The whole narrative hinges on the notion that simply sharing a name with someone can implicate you in their life and change your destiny.
Politics
Throughout the film, different characters are referred to by their political persuasions as a way of indicating something deeper about their identity and their response to conflict. The Dude is identified as a pacifist, the German ransom-seekers as nihilists, and the Malibu cop who arrests the Dude is a fascist. These different political persuasions are framed as philosophies of life, and are tightly connected to each character's identity. Additionally, the millionaire Lebowski represents a greedy and corrupt Republican, posing as a generous philanthropist, but embezzling funds from his charitable organization and insisting on the importance of personal responsibility.
Going with the flow
Part of what makes Dude such an endearing and comic hero is that in the midst of a great deal of stress, tension and conflict, he maintains a groovy pacifistic attitude. Even when his life is on the line, he chooses to let off some steam by smoking some marijuana and enjoying the sensual pleasures of life. The Dude represents the idea of "going with the flow" and while his journey is rocky, his flexibility pays off in the end and he survives. The theme of going with the flow is also typified by the Stranger who appears at the bowling alley and sagely says, "Sometimes you eat the bear, and sometimes the bear eats you."
Money
Throughout the film, the characters are all in search of money. The dude needs money to pay his rent, and he needs money to clean the pee stain on his rug. When it seems like Bunny has been kidnapped, Lebowski needs money to give to her kidnappers as ransom. The Dude loses that money in an elaborate plan made by Walter to give the kidnappers a "ringer," or a fake briefcase with money in it. Throughout the rest of the movie, we follow the Dude as he searches for the lost briefcase with the million dollars in it, only to find out later that there was no ransom money, that Lebowski was embezzling money all along for his own purposes.
Reproduction
While it is not often referred to in the film, a major theme is reproduction. After Maude seduces the Dude and they are lying in bed, she informs him that she slept with him in order to conceive a child. She chose him as the father because she knew he would not be involved with the child's life and she does not have to worry about running into him in the future. The Dude is shocked, but not altogether upset about learning of Maude's motives and it is not referred to again. Then, at the end, the Stranger tells us that Maude is pregnant with the Dude's child, and uses this news as a kind of consolation for the fact that Donny recently passed away. Reproduction and birth become the promise of the future, a way of having hope for things to come.
Deceit
The whole arc of the plot is based around a lie, as we find out at the end. Lebowski has been lying the whole time about his motives, and the nihilists who claim to have kidnapped Bunny are also lying. Lebowski feigned wanting Bunny back at all, and sent the Dude to hand over an empty briefcase as the ransom money, and embezzled money from his own foundation to live off. Meanwhile, the nihilists never kidnapped Bunny at all, but were just trying to con a millionaire out of his millions.
Drugs and Alcohol
Drugs and alcohol are not stigmatized in the film. Rather, they are part of the fabric of the Dude's life. Throughout, he can often be seen either smoking a joint or drinking his signature cocktail, a White Russian, and this represents just how relaxed and unflappable the Dude is. He lives a casual life of leisure, and substances help him achieve his even-keeled Zen state.
