A disc brake, in particular, for a commercial vehicle, has a brake caliper which engages over a brake disc, brake linings which make contact with the brake disc in a functional position, and a brake application device with which one of the brake linings can be pressed, via at least one adjusting spindle, against the brake disc. An adjustment device is rotationally fixed to the adjusting spindle, by which wear-induced change in the running clearance between the brake lining and the brake disc can essentially be compensated. A closure lid covers the adjustment device and is attached to the brake caliper. A lining wear sensor communicates with a step-down gear mechanism connected to the adjusting spindle. The lining wear sensor is embodied as a contactless sensor which rotates on a concentric path has its change in angular position detected by the lining wear sensor and transmitted to an evaluation device.