"My Last Duchess" - How is the character of the Duke slowly revealed in the poem?

This historic poem, "My Last Duchess", was written by Robert Browning in the middle of the nineteenth century, more precisely, in the year of 1842. This dramatic monologue is written in rhyming couplets, but the poem is so well thought of and so well structured that the reader/listener doesn't even notice the rhyming sounds. During the poem, the Duke of Ferrara is speaking to an envoy of a Count, do discuss and arrange an agreement …

…there's something wrong going on about his dead wife. I think this is an excellent, brilliantly-structured poem, which fully reflects the inner thoughts and feelings of the Duke. The reader is put into the position of a detective, as the writer builds up tension and the reader starts to suspect at the end that it was him, the Duke, which killed his own wife, in order to own her, to have her only for himself.