PACS 75.47.De, 75.70.Cn Since the discovery of the giant magnetoresistance (GMR) in magnetic multilayers, several theoretical descriptions have been used to determine the resistivity of such layered structures. The resistance for the current in direction of the planes of layers can easily be measured, and has been intensively studied theoretically. However, the investigation of the GMR for the current perpendicular to the planes (CPP) is slightly more difficult. Here, a microscopic formalism for the study of the CPP GMR is reported by making use of the Kubo -Greenwood equation. Within this method perturbations of the interfaces like interdiffusion, alloy formation, or impurities can easily be included, which is of importance, because the discussion of the GMR is always related to the structure of the interfaces. The presentation of the KuboGreenwood formalism for CPP transport is complemented by a brief discussion of some exemplary results.