Alignment of the Silicon Detectors of the ATLAS Experiment The ATLAS Experiment is one of the four large detectors located at the Large Hadron Collider at CERN in Geneva, Switzerland. Data taking of ATLAS is expected to start in 2007. The reconstruction of particle tracks is performed by silicon and drift tube based subdetectors. In order not to degenerate the track measurements the position of the silicon detector elements have to be known to a precision better than about 10 micrometers. This precision can be achieved by track based alignment algorithms combined with measurements from hardware based alignment techniques. The proposed alignment algorithms for the ATLAS inner detector and their implementation into the common ATLAS software framework are presented. First results from a testbeam setup and from cosmic ray data are shown and discussed.