What are the rules in pronoun-antecedent agreement?

There is only one rule for pronoun-antecedent agreement: that the pronoun used must agree in number (singular, plural) and gender (male, female, neuter) with the noun antecedent.

Example:

Judge John Lee insists on proper dress in his courtroom. (the pronoun 'his' agrees with the noun antecedent, Judge John Lee, one person, a male)