  Antihydrogen, the simplest pure-antimatter atomic system, holds the promise
of direct tests of matter-antimatter equivalence and CPT invariance, two of the
outstanding unanswered questions in modern physics. Antihydrogen is now
routinely produced in charged-particle traps through the combination of plasmas
of antiprotons and positrons, but the atoms escape and are destroyed in a
minuscule fraction of a second.
  The focus of this work is the production of a sample of cold antihydrogen
atoms in a magnetic atom trap. This poses an extreme challenge, because the
state-of-the-art atom traps are only approximately 0.5 K deep for ground-state
antihydrogen atoms, much shallower than the energies of particles stored in the
plasmas. This thesis will outline the main parts of the ALPHA experiment, with
an overview of the important physical processes at work. Antihydrogen
production techniques will be described, and an analysis of the spatial
annihilation distribution to give indications of the temperature and binding
energy distribution of the atoms will be presented. Finally, we describe the
techniques needed to demonstrate confinement of antihydrogen atoms, apply them
to a data taking run and present the results, making a definitive
identification of trapped antihydrogen atoms.
