Learn German: Der König traf den Herzog und dessen Sohn.

If the sentence said seinen Sohn, the possessive would refer back to the subject of the sentence, meaning the king met his own son. By using the demonstrative pronoun dessen (literally "of that one"), it clearly refers to the other person just mentioned: the duke's son.

How do we know to use dessen rather than deren?

The pronoun must match the gender of the possessor, not the thing being possessed. Because der Herzog (the duke) is masculine, we use the masculine genitive form dessen. If the possessor were feminine or plural, we would use deren.

The son is the direct object being met. Why isn't there an accusative ending on dessen?

Unlike regular possessive adjectives (like seinen), the demonstrative pronouns dessen and deren do not take grammatical endings to match the noun that follows them. They are fixed in their genitive forms. So, even though Sohn is in the accusative case here, dessen stays exactly as it is.

Herzog is a title for a male person. Why isn't it an n-noun like den Prinzen?