There is increasing interest in using particle accelerators to form very intense beams of high-energy muons. However, due to its short average lifetime (2.2 microseconds), it has not been possible to accelerate a muon beam. A key step in demonstrating the feasibility of muon accelerators is the Muon Ionization Cooling Experiment (MICE). The main obstacle to accelerating an intense muon beam is that the way such beams are created makes them too large to fit into the vacuum chamber of a synchrotron, and the short muon lifetime leaves little time to shrink the beam. Ionization cooling is a new technique to shrink, or cool a muon beam quickly. The goal of MICE is to build a section of an ionization-cooling channel, instrument it to measure its cooling performance, and use a muon beam produced at a particle accelerator to demonstrate that it works as designed. A collaborative effort of some 150 physicists and engineers from Europe, Asia, and the US, MICE is being mounted at England's Rutherford Appleton Laboratory. Construction of the apparatus is currently in progress, and the running of the experiment and analysis of its results is expected to take place during the 3-year period of the grant proposed here. This proposal requests renewal funding for the Illinois Institute of Technology MICE group in support of continued US leadership in muon cooling and in the muon accelerator facilities that might be constructed, in the US or elsewhere, once the feasibility of ionization cooling is demonstrated. The broader impact of this work is most evident in the use of an accelerated muon beam for a Neutrino Factory recognized as the most powerful tool yet conceived in the quest to understand the mysterious oscillatory behavior of the neutrino and its possible role in the evolution of the matter-dominated Universe in which we live. In addition, the pace of MICE development, running, and analysis is particularly well suited to the training of students. MICE will take approximately three years to complete, a good fit to the typical physics student?s graduate training.