An ensemble of cylindrical barrel detectors that surround the nominal interaction point is used to track all the particles that fly out of the hot, dense medium. The Inner Tracking System(ITS) (consisting of three layers of detectors: Silicon Pixel Detector(SPD), Silicon Drift Detector(SDD), Silicon Strip Detector(SSD)), the Time Projection Chamber(TPC) and the Transition Radiation Detector(TRD) measure at many points the passage of each particle carrying an electric charge and give precise information about the particle's trajectory. The ALICE barrel tracking detectors are embedded in a magnetic field of 0.5 Tesla produced by a huge magnetic solenoid bending the trajectories of the particles. From the curvature of the tracks one can derive their momentum. The ITS is so precise that particles which are generated by the decay of other particles with a long(~.1 mm before decay) life time can be identified by seeing that they do not originate from the point where the interaction has taken place (the "vertex" of the event) but rather from a point at a distance of as small as a tenth of a millimeter. This allows us to measure, for example, bottom quarks which decay into a relatively long-lived B-meson through "topological" cuts.