A resolution (also called denouement) in literature refers to the conclusion of a story's plot. It normally occurs at the end of the falling action when the story slows down and all or most problems or issues have been resolved. A story in which all the conflicts have been solved is said to have a complete end and a strong resolution.
The resolution in Julius Caesar occurs with the deaths of Brutus and Cassius and the defeat of their armies. The chief conspirators have both committed suicide: Cassius asks his manservant, Pindarus, to stab him in Act 5, Scene 3, while Brutus runs onto his sword, which is held by Strato, in Scene 5. His death is followed by the arrival of Antony and Octavius. Those of their followers who are still alive surrender to Antony and Octavius.
Both generals have decided to take their own lives since suicide is deemed more honorable than suffering the shame and degradation of surrendering to one's enemy. Their deaths are seen as noble, and Antony extends great praise to Brutus for his honor, courage, integrity, and goodness.
This was the noblest Roman of them all:
All the conspirators save only he
Did that they did in envy of great Caesar;
He only, in a general honest thought
And common good to all, made one of them.
His life was gentle, and the elements
So mix'd in him that Nature might stand up
And say to all the world 'This was a man!'
Antony and Octavius's arrival pertinently indicates that all conflicts have been resolved, and Octavius's final words are a fitting conclusion to the play:
So call the field to rest; and let's away,
To part the glories of this happy day.
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The resolution is a little unsettling, since so many of the characters have died by the end of the play. Caesar, Brutus, and Cassius are all dead, and many more have died in the battles that ensued after Caesar's murder.
The resolution, though, comes in the idea that hope, and Rome, will live on. Octavius and Antony are left to lead Rome into the future, and the reader can hope that they will have learned from the preceding events and carry that knowledge on with them.