What are the inciting action and rising action of the play Hamlet?

The inciting action or incident that sets the plot of Hamlet into motion is Hamlet's encounter with his father's ghost. The ghost tells Hamlet that Claudius, Hamlet's uncle and now Denmark's ruler, murdered him, and says that Hamlet must avenge his death. It is not everyday that one encounters a ghost, especially one who delivers such a bombshell as this one does, so a gripping inciting incident starts the drama.

The rising action includes, paradoxically,...

The inciting action or incident that sets the plot of Hamlet into motion is Hamlet's encounter with his father's ghost. The ghost tells Hamlet that Claudius, Hamlet's uncle and now Denmark's ruler, murdered him, and says that Hamlet must avenge his death. It is not everyday that one encounters a ghost, especially one who delivers such a bombshell as this one does, so a gripping inciting incident starts the drama.

The rising action includes, paradoxically, Hamlet's initial inaction, which is integral to how the final tragedy unfolds. A more impulsive character, say a Laertes or a Romeo, would simply rush in, kill the uncle and be done with it, giving the uncle no time to maneuver. Not so Hamlet. He contemplates what has happened. Part of the rising action is his questioning of the motives of the apparition he saw. Was it really his father's ghost telling him the truth or was it a demon tempting him to kill an innocent man? Hamlet's experiment to find out the truth, having actors enact his father's supposed murder in pantomime to gauge Claudius's reaction to it, tips off Claudius, as does Hamlet's mistaken murder of Polonius. Polonius's death also contributes to the rising action by propelling Laertes back to Denmark to kill Hamlet. When Hamlet also appears back in Denmark, having foiled his uncle's plot to have him murdered, the scene is set for the final tragedy. Claudius manipulates Laertes into a duel with Hamlet and introduces poison to tip the balance in favor of Laertes. This leads to the final climax in which the stage ends up strewn with corpses.