These are the proceedings of the Workshop on Precision Measurements of alphas held at the Max-Planck-Institute for Physics, Munich, February 9-11, 2011. The workshop explored in depth the determination of alphas(mZ) in the MS-bar scheme from the key categories where high precision measurements are currently being made, including DIS and global PDF fits, tau-decays, electroweak precision observables and Z-decays, event-shapes, and lattice QCD. These proceedings contain a short summary contribution from the speakers, as well as the lists of authors, conveners, participants, and talks.