Appeals to the board of adjustment may be taken by any person aggrieved, by any neighborhood organization as defined in section 32.105 representing such person, or by any officer, department, board or bureau of the municipality affected by any decision of the administrative officer. Such appeal shall be taken within a reasonable time, as provided by the rules of the board, by filing with the officer from whom the appeal is taken and with the board of adjustment a notice of appeal specifying the grounds thereof. The officer from whom the appeal is taken shall forthwith transmit to the board all the papers constituting the record upon which the action appealed from was taken. An appeal stays all proceedings in furtherance of the action appealed from, unless the officer from whom the appeal is taken certifies to the board of adjustment after the notice of appeal shall have been filed with him that by reason of facts stated in the certificate a stay would, in his opinion, cause immediate peril to life or property. In such case proceedings shall not be stayed otherwise than by a restraining order which may be granted by the board of adjustment or by a court of record on application or notice to the officer from whom the appeal is taken and on due cause shown. The board of adjustment shall fix a reasonable time for the hearing of the appeal, give public notice thereof, as well as due notice to the parties in interest, and decide the same within a reasonable time. Upon the hearing any party may appear in person or by agent or by attorney.