Shakespeare's Julius Caesar is a play about a conspiracy to assassinate a fundamentally sympathetic tyrant. Unlike Macbeth, for example, who by the end of the play is a purely evil tyrant who the audience feels deserves to die, Julius Caesar is a generally sympathetic figure. Even if he is imperfect, tending towards arrogance, he is a popular leader, skilled general, and honest and capable administrator. The conspirators form two groups, Brutus, who deeply loves Caesar but loves the Republic even more, and feels that killing Caesar is the only way to prevent Rome from lapsing from Republic into monarchy, and the other conspirators, who either have personal grudges against Caesar or who are members of the patrician party which has lost power due to an alliance between Caesar and the plebeians. The conspirators agree that they will all stab Caesar to share responsibility for his death.
Casca stabs Caesar first, then the other conspirators stab him, and Brutus stabs him last.