Final answer:
Casca, Brutus, and Cassius discuss the plan to assassinate Julius Caesar due to concerns over his potential tyranny and the impact on the Roman Republic, with Cassius persuading Brutus to join the conspiracy.
Step-by-step explanation:
The main topic of conversation in the conversation of Casca, Brutus, and Cassius in Shakespeare's play Julius Caesar is the plotting of Julius Caesar's assassination and discussions on the nature of Caesar's ambition and power. These conspirators, as well as others in the play, express concern over Caesar's rising influence and potential to become a tyrant.
Brutus, in particular, is torn between his friendship with Caesar and his fear that Caesar's rule could harm the Roman Republic. Cassius plays a significant role in persuading Brutus to join the conspiracy, playing on Brutus's sense of honor and the notion of acting for the greater good of Rome.