She attended the fund-raiser 'at the invitation of' the committee chairperson. [=she attended because she was invited by the committee chairperson]
You have a 'standing/open invitation' [=you are always welcome; you are always invited] to visit us any time.
The event is 'by invitation only'. [=only people who have been invited to the event can attend it]
(..) which you took... ...in exchange for her having an audience with these noble men? - That is a lie. - Is it? Was he not, by your invitation, asked to come to the king's bedchamber? The very bed where you attempted to negotiate with me so vigorously? You look shocked. (..)2006 300