A hamlet is (usually — see below) a small settlement.
In British geography, a hamlet is defined ecclesiastically. It is a village that may or may not have its own church, but which does not form a parish in its own right.
In the U.S. state of New York, hamlets are unincorporated areas within towns. Unlike villages, New York hamlets are not legal entities, and have no officially defined boundaries or government. They rely on the surrounding town for all municipal government services. See Political subdivisions of New York State.
In numerous provinces in Canada, there are officially designated municipalities, generally smaller than villages, classified as hamlets. A notable example is Sherwood Park, Alberta, which has a population of more than 70,000 – well above that needed for city status – but which has retained hamlet status.
Hamlet's condemnation of it as "incest" is not, it seems, the general opinion of the court and Claudius himself confesses to Laertes that "As the star moves not but in his sphere..I could not but by her."
Hamlet, too reminds the audience twice how Gertrude behaved in the presence of his dead father, which serves to emphasise the fickleness she has shown since the King's death.
When Hamlet dies Horatio plans to die with him, intending to drink what is left of the poison wine, but Hamlet trusts his friend to be his dying voice and gives Horatio the task of telling the story of what happened and setting the record straight.