Pronouns (and nouns) in English display "case" according to their function in the sentence. Their function can be:
The following table shows the different forms for pronouns depending on case.
A problem of case: Mary and I or Mary and me?
In 1, Mary and I are subjects, which is why the pronoun takes the subjective case ("I"). In 2, Mary and I are objects, which is why the pronoun takes the objective case ("me"). An easy way to check the correct case is to try the sentence without Mary. Would you say "I am delighted to be here" or "Me am delighted to be here"? Would you say "The letter was addressed to me" or "The letter was addressed to I"?