Experimental particle physics is on the verge of a new era, heralded by the Large Hadron Collider being commissioned at the European Center of Nuclear Research, CERN, located just outside of Geneva, Switzerland. The LHC accelerator will collide protons at a center of mass energy of 14 TeV, opening up a new window for particle discoveries and precision measurements of existing theories. Particle detectors are located at four beam crossings along the LHC, one of which is the ATLAS detector. This is the largest of the LHC experiments, employing a great variety of detector and magnetic field technologies to identify a wide range of particles. The complex magnetic field and high collision rate, however, make the reconstruction of particle tracks very challenging. Things are complicated further by the relatively big amount of material within ATLAS, generating considerable disturbances to the particle tracks through material interactions such as energy loss and multiple scattering. In this thesis we present an algorithm, Simultaneous Track and Error Propagation (STEP), which addresses these track reconstruction challenges.