(a) The government of each county shall create a library agency as a part of the executive branch of county government and, in accordance therewith, shall have the power:
(1) To establish and administer a county library system offering to residents of the county access to services and resources and guidance in their use. Each county may create a countywide library system offering free and equal access to such services and resources to every resident of the county, or each county may create library districts within the county supported by taxes levied upon real property within said districts as provided for in this chapter providing that county residents who are not residents of a library district shall have access to such library district's services and resources upon payment of a fee set by ordinance of the county;
(2) To receive, by taxation or otherwise, accept, administer and expend any money, materials or other aid granted, appropriated or otherwise provided by local, state or federal governments, or by any source, public or private, in accordance with the terms thereof, for the purposes provided in this chapter;
(3) To perform all other activities pertinent to the organizational function of the library agency.
(b) The county executive or President of Levy Court, whichever applies, upon the approval of the county library advisory board, may appoint a county library administrator who shall be referred to as county librarian, or the county library manager in New Castle County, who shall be the administrator of the county library agency.