From what point of view is the poem, "My Last Duchess," written?
This poem uses a first person subjective point of view. This means that it is narrated by a participant in the story, someone who uses the first person pronoun "I," and that it is narrated in the present tense, as events occur. Though the duke is telling a representative of the count, whose daughter he now wishes to marry, of some events in the past -- as regards the life of his last duchess who is now dead -- the text occurs in the present, as he is negotiating the terms of his next marriage.
It is, actually, the duke's ability to so blithely pass between a discussion of his now-dead wife to the present that makes him such a chilling figure. Near the poem's end, he says,
"I gave commands; / Then all smiles stopped together. There she stands / As if alive. Will’t please you rise? We’ll meet / The company below, then."
In other words, dissatisfied with the too-joyful behavior of his former wife, he "gave commands" -- either to her, to stop being so uniformly happy with everything, or perhaps even to have her killed so that he could start afresh with someone new -- and so "all smiles stopped" because she died. In the next breath, he's back to the present, asking this man to come downstairs with him and rejoin their party. It's quite disturbing, really, and this particular point of view helps make it possible.
Robert Browning's poem "My Last Duchess" is what is known as a dramatic monologue. It consists of an extended speech given in the voice of a first person narrator, the Duke of Ferrara. It is set in Renaissance Italy. He is addressing an envoy sent by a count to negotiate the terms on which the Duke will marry the Count's daughter. As the Duke talks, he appears to be showing the Count's envoy around his castle. The point of this tour is probably to impress the envoy with his wealth and good taste (what is sometimes called "cultural capital").
The Duke had been married in the past and is now a widower. The poem suggests, although does not absolutely confirm, that the Duke may have killed his previous wife.
Browning uses the dramatic monologue to have characters, in a sense, incriminate themselves. Although the Duke is trying to impress his immediate audience, the longer he speaks, the more we find him cold-hearted, jealous, and even cruel in the way he thinks of his deceased wife as a possession rather than as a person.