How is αὐτος used in Greek?

The word αὐτος has three different meanings in Greek, depending on its case and the use of the definite article.1) When the word agrees with an article + noun but is not sandwiched, it means himself/herself/itself/themselves.ὁ βασιλευς αὐτος = The king himselfαὐτος ὁ πατηρ = The father himselfThe word also has this meaning when it appears on its own as a pronoun in the nominative:αὐτη ἐφυγεν = She herself fled.2) When the word agrees with an article + noun and is sandwiched, it means the same. This is always the meaning when a part of αὐτος comes immediately after the article.τους αὐτους δουλους εἰδεν = He saw the same slaves.3) When the word is used on its own as a pronoun and is not in the nominative, it means him/her/it/them. It is always third-person, and cannot come as the first word of a sentence or clause.ὁ στρατηγος αὐτην εἰδεν = The general saw her.ὁ ἀγγελος αὐτοις ἐπιστευεν = The messenger trusted them.