Robust constraints on varying fundamental constants from QSO absorption systems

The coupling constants of the fundamental forces are among the most precisely measured and yet most poorly understood aspects of modern physics. There is currently no explanation for why these 'fundamental constants' have the values we observe, or even if they should be constant. This thesis aims to minimize and understand systematic errors in measuring fundamental constants by introducing a new method to search for wavelength-dependent velocity shifts between pairs of quasar spectra. This method is applied to existing and new spectra from three different 8-10m telescopes: Keck, the Very Large Telescope, and Subaru.