Antimatter provides unique opportunities in science and technology, ranging from fundamental tests of the symmetries of nature to the study materials and human metabolism. This symposium explores forefront science with positrons (the antiparticles of electrons), antiprotons, antiatoms, and the most complex antinuclei yet observed. Current and future uses of positron emission tomography (PET) will be described, including studies of human metabolic processes. Work at a new intense positron beam facility will also be described that is designed to study new materials such as those used for high-speed electronics. The attachment of positrons to ordinary matter will be discussed -- work toward establishment of the principles of a chemistry of matter and antimatter. The first studies of a many-positron, many-electron system, the positronium molecule (i.e., e+e–e+e–), will also be described. This is a key step in the creation of a quantum gas of positrons and electrons, with potentially far-reaching consequences ranging from a new, ultrasensitive matter interferometer to an annihilation gamma-ray laser. The latest experiments will be described that are designed to trap and study antihydrogen (i.e., a stable antiatom consisting of a bound antiproton and positron). Recent experiments at the Relativistic Heavy Ion Collider have observed complex antinuclei of unprecedented complexity, yielding new insights into the dynamics of the quark-gluon plasma.