At the time of Muhammad () one could say that the Islamic government had his base in Medina or wherever he actually was. As far as I know there were no state officials nor a treasury etc. these kinds of things have come later due to the extension of the "Empire" and other facts.
To make this question reasonably focused: I'd like to have a list of the major introductions in terms of the public administration that have been created during the time of the four Rashidi caliphs () and the necessity leading to it!
Historical evidences are highly appreciated.