What are the main conflicts in the story and how are they resolved?

Pride and Prejudice, by Jane Austen, is a novel fraught with conflict from the beginning, even from the first line: "It is a truth universally acknowledged, that a single manin possession of a good fortune, must be in want of a wife." Austen's tone here is ironic, indicating cultural conflicts between prudential marriage (arranged marriages to preserve estates and bloodlines) and companionate marriages (for love and personal fulfillment). This is an abstract conflict, and is only partially resolved in the novel. When Darcy eventually weds Elizabeth Bennet, he does so for love, but she is not truly outside the realm of a socially appropriate mate. (She notes, in a conversation to Lady de Bourgh, that Darcy is a gentleman and she a gentleman's daughter.) Austen gently pushes people's ideas of a suitable mate without being truly radical about it.

More concrete examples of conflict are between Elizabeth Bennet and Darcy when they disagree about behavior in general on several separate occasions. This is eventually resolved when Darcy admits to his shortcomings and changed behavior as he proposes (again) to Elizabeth.

Also, Elizabeth Bennet has conflict with her father about appropriate behavior regarding parenting and childrearing when they discuss the possibility of Lydia away to Brighton with the regiment. This is badly resolved when Lydia does wind up acting entirely inappropriately by running away with Wickham to London. Darcy has to resolve the situation by forcing Wickham into marriage with Lydia.

Elizabeth Bennet has direct conflict with Lady Catherine de Bourgh, Darcy's aunt, when Lady Catherine comes to visit Elizabeth and demands she promise to never marry Darcy. This is never really resolved, but does serve as an important plot device: when Elizabeth won't make the promise to Lady Catherine, and Catherine complains to Darcy about it, he has knew hope and proposes to Elizabeth the second time.

The conflicts that exist in the text are generally addressing social behaviors. The tension between tradition and progress, vulgarity and refinement, and duty to one's community/family vs. personal fulfillment is seen in the conflict.