The CERN's Large Hadron Collider (LHC) is the world largest particle accelerator. ATLAS (A Toroidal LHC ApparatuS) is one of the two general purpose experiments equipped with a charged particle tracking system built on two technologies: silicon and drift tube based detectors, composing the ATLAS Inner Detector (ID). The alignment of the tracking system poses a challenge as one should solve a linear equation with almost 36 000 degrees of freedom. The required precision for the alignment of the most sensitive coordinates of the silicon sensors is just few microns. This limit comes from the requirement that the misalignment should not worsen the resolution of the track parameter measurements by more than 20%. Therefore the alignment of the ATLAS ID requires complex algorithms with extensive CPU and memory usage. So far the proposed alignment algorithms are exercised on several applications. We will present the outline of the alignment approach and results from Cosmic Ray runs and large scale computing simulation of physics samples mimicking the ATLAS operation during real data taking. For the later application the trigger of the experiment is simulated and the event filter is applied in order to produce an alignment input data stream. The full alignment chain is tested using that stream and alignment constants are produced and validated within 24 h. Cosmic ray data serves to produce an early alignment of the real ATLAS Inner Detector even before the LHC start up. Beyond all tracking information, the assembly survey database contains essential information in order to determine the relative position of one module with respect to its neighbors. Finally a hardware system measuring an array of grid lines in the modules support structure with a Frequency Scan Interferometer monitors short time system deformations.