The governing body of any city of the first class, city of the second class, or village may by ordinance create a limited street improvement district for the sole purpose of grading, curbing, and guttering any unpaved street or streets or curbing and guttering any paved or unpaved street or streets in the city or village and each district shall be designated as Street Grading, Curbing, and Guttering District No. ..... or as Curbing and Guttering District No. ...., as the case may be. The city clerk or village clerk shall, after the passage, approval, and publication of such ordinance, publish notice of the creation of any such district or districts one time each week for three weeks in a legal newspaper in or of general circulation in the city or village. After the passage, approval, and publication of such ordinance and the publication of such notice, the procedure of the mayor and city council or chairperson and village board of trustees in reference to such improvement shall be in accordance with the applicable provisions of sections 16-620 to 16-655 or 17-508 to 17-520.