Cassius is trying to get Brutus to join the conspiracy to kill Caesar. Brutus isn't really all for it at first, but eventually gives in as time goes on. Cassius gets him to believe that if Caesar is king, things will fall apart. "Into what dangers would you lead me, Cassius, that you would have me seek into myself. For that which is not in me?" (l:iii:ln 63-65)
Act 4: Sc 3
Artemidorus made a letter to Caesar about the conspirators and there plan to kill him. Caesar read the letter and blew him off. He believes his so called "friends" would never do that. "Here will I stand till Caesar pass along, and as a suitor will I give him this" (2:iii:ln 10-11)
Act 5: Sc 5
Conspirators kill Caesar at the senate. They kill Caesar because they suspect he may become a tyrant. He tries to explain they've got the wrong guy, but they're convinced he's the bad person.
Caesar's ghost comes to Brutus and says he'll see Brutus on the battlefield, accurately translates to he'll die. Brutus is a bit shooken up from this. He's basically like "See you then, i guess".
Octavius and Antony win the battle and plan a proper burial for the both of them. Cassius ended up taking his life over a rumor that Titinius did when he really faked it. Brutus ended up taking his life also so Caesar would let it all go.