Final answer:
Claudius's hesitation to act against Hamlet arises from the prince's popularity, their familial relationship, perceived madness, and the need for a justifiable pretext, leading to a battle of wits and espionage between them.
Step-by-step explanation:
The reasons why Claudius did not take immediate actions against Hamlet in Shakespeare's play can be multifaceted. Principally, Claudius is aware that Hamlet is highly popular among the people of Denmark, and any rash action against him could lead to public discontent or even rebellion. Additionally, Claudius is related to Hamlet by blood, being his uncle, and married to Hamlet's mother, which makes any decision against Hamlet more complicated due to these familial ties. There's also the fact that Hamlet's erratic behavior, which is perceived as madness by many at court, makes Claudius hesitant to act directly as it could prompt speculation or sympathy towards Hamlet. Instead, Claudius opts for spying and manipulation to try to uncover Hamlet's true intentions and find a solid pretext for action that would seem justifiable to the court and the people. This culminates in a series of espionage and counter-espionage between Hamlet and Claudius, revealing the depth of deceit and calculation in their struggle.