a fastening system including a plurality of fastening modules to mount a solar module having a first longitudinal direction on a roof structure or a façade having a second longitudinal direction . each fastening module comprises one module carrier mountable on the roof structure or on the façade ; a slide block guidable inside the module carrier ; a module clamp ; and a fastener to connect the module clamp to the slide block to clamp a respective solar module between the module clamp and the slide block . the module clamp is rotatable between two positions on the fastener so that an arrangement of the fastening modules permits the solar module to be mounted on the roof structure or the façade with the first longitudinal axis perpendicular or parallel to the second direction .