Axions are hypothetical particles that, if detected, could solve two outstanding problems of particle astrophysics, the nature of dark matter and the CP invariance of strong interactions in the standard model. There is only one experiment in the world that has taken data in the search for axion dark matter, and that is the ADMX axion experiment in the U.S.A. This experiment was the subject of my Ph.D. dissertation at the Massachusetts Institute of Technology.