An exposure apparatus comprising a holding part for holding an electric discharge lamp, the electric discharge lamp includes an electric discharge tube which covers an electric discharge space in which a pair of electrodes are disposed to face each other, a socket provided on one end of the electric discharge tube, a metal member which guides one of the pair of electrodes into the socket, wherein an opening for ventilation is provided in a bottom of the socket, the holding part includes a ventilation pipe to form a path for ventilation through the opening in the bottom of the socket, and a cooling part for cooling the metal member by supplying a cooling medium to the metal member through the ventilation pipe.