A mirror module for fastening to a structural element, comprises a mirror arrangement that includes at least one mirror stack and a first receiving device for holding the mirror arrangement. Each of the at least one mirror stack comprises at least one individual mirror made of a first material. The first receiving device is made of a second material which has a coefficient of thermal expansion adapted to the first material. For fastening the mirror module to the structural element, a second receiving device made of Invar is provided which holds the first receiving device of the mirror module.