Besides the obvious conflict between Ceasar and the senate, there are a multitude of internal conflicts throughout the play.
1. Cassius is jealous of Caesar's glory. This is not the same as the political conflict; this one's personal. Cassius remembers times when Caesar was weak (when he was ill, when he nearly drowned, etc), and Cassius believes that he is not getting the proper respect he deserves.
2. Marcus Brutus is Caesar's close friend, and Brutus is torn between love for his country and love for his friend. Love for country wins out, and Brutus joins the conspiracy.
3. Calpurnia, Caesar's wife, had a bad dream and doesn't want him to go to the Senate House, but to stay home instead. Caesar almost gives in until Decius Brutus reinterprets the dream to seem more favorable. Decius also reminds Caesar that he doesn't want to be viewed as one who gives into his wife's fears, does he?
4. Brutus and his wife Portia are in conflict because Brutus won't tell her what's going on. She knows something's up, but Brutus thinks that she is better off in the dark. This puts a wall between the two as she even says she'll stab herself in the thigh to prove just how tough she is.
5. Brutus is tormented by his conscience after the assassination, and his guilt feelings materialize as Caesar's ghost.
6. Brutus and Cassius begin fighting after the assassination about money to fund the battle and just where Cassius got the funds.
The most obvious "major" conflict is the one between Caesar and the senate. Caesar is growing more powerful every day, and some of the senators fear that their jobs are on the line. They don't want Caesar to become king because all the power would then be centered in him. How is this conflict resolved? Murder.
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