  CERN announced in January 1996 the detection of the first eleven atoms of
antimatter ever produced. The experiment was based on a method proposed earlier
by S. Brodsky, C. Munger and I. Schmidt, and which furthermore predicted
exactly the number of atoms that were detected for the particular conditions of
the experiment. The study of antihydrogen affords science the opportunity to
continue research on the symmetry between matter and antimatter. In this talk
the importance of antihydrogen as a basic physical system is discussed.
Different production methods that have been tried in the past are briefly
presented, and the method that was used in the CERN experiment is analyzed in
detail. It consists in producing antihydrogen by circulating a beam of an
antiproton ring through an internal gas target. In the Coulomb field of a
nucleus, an electron-positron pair is created, and antihydrogen will form when
the positron is created in a bound rather that a continuum state about the
antiproton. The theoretical calculation of the production cross section is
presented in detail. A discussion of the detection systems used both in the
CERN experiment and in another similar experiment that is right now underway at
Fermilab are also given. Finally I present and discuss possible future
experiments using antihydrogen, including the measurement of the antihydrogen
Lamb shift.
