The legislative body of any municipality may establish or operate a public library and reading room, together with such kindred apartments and facilities as the legislative body approves; and may levy a tax annually on all taxable property of the municipality for the establishment or operation of a public library. Such tax shall be levied and collected as other taxes, and shall be known as the “library fund”. Such library and reading room shall be free to the use of the inhabitants of the city, subject to such reasonable rules and regulations as the board of trustees may adopt in order to render the use of the library and reading room of the greatest benefit. Such board may exclude from the use of such library and reading room any person who wilfully violates such rules, and may extend its privileges to persons residing in this state outside the city upon such terms and conditions as it may prescribe.