What is the difference between Stiva's understanding of the world and Levin's understanding of the world in Anna Karenina?
Anna Karenina, by Leo Tolstoy, is primarily Anna's story; however, Stiva and Levin are also primary characters who serve as foils to one another throughout the novel. In nearly every way, their world views are polar opposites.
Stiva is careless and frivolous and free with his words and his affections. He spends money he does not have (and does not intend to repay) and is always looking for ways to make money without working for it. He is not a faithful husband but he is a faithful friend as long as it suits him; he likes the excitement and energy of living in a big city and is primarily concerned with his own pleasures of the moment.
Levin, on the other hand, is careful about nearly everything in his life: his money, his affections, his land, his words. He is a good steward of his estate (so good, in fact, that others entrust him with their fiscal affairs) and is willing to work hard to achieve his goals. He is generally a loner and struggles with most relationships in his life because he is unaccustomed to speaking what he feels. Levin is faithful to a fault and uncomfortable when he is away from the land.
The two men are consistently juxtaposed throughout the novel. At one point, Levin is literally supporting Stiva's family, and Stiva is perfectly content to let him. Levin has a sense of responsibility which Stiva admires but has no desire to emulate. Stiva is a careless man and looks even worse when compared to the careful Levin.
Levin has a much more humble approach to the world, while Stiva is more concerned about living happily. Levin knows that hard work, persistence, and kindness are what will get an individual what they want, which is usually happiness, a family, and a good living. Stiva, on the other hand, wishes only to "enjoy life" by throwing parties, going on trips, having mistresses, etc. Levin is also very accountable for his actions, while Stiva usually is not.