These two volumes collect forty-four selected papers from the scientific contributions presented at the Third European Workshop on Quantum Systems in Chemistry and Physics, held in Granada (Spain), April 19–22, 1998. Ninety-nine scientists from Bulgaria, Columbia, Cuba, Denmark, Finland, France, Germany, Hungary, Israel, Italy, Mexico, Netherlands, Norway, Poland, Russia, Slovakia, Spain, Sweden, United Ki- dom, Uruguay and Venezuela attended the workshop, discussing the state of the art, new trends, and future evolution of the methods and applications. The workshop took place at the ‘Los Alixares’ Hotel, where 45 lectures were given by prominent members of the scientific community; in addition, 49 posters were presented in two very animated sessions. The success of this workshop is due, without doubt, to the excellent tradition initiated at the previous workshops, organised by Prof. R. McWeeny in San Miniato, Pisa (Italy), 1996, and by Prof. S. Wilson in Oxford (United Kingdom), 1997. These workshops create occasions for meetings and disc- sions on the current state of the art, emerging methods and applications and new trends in this area of science. The three meetings were sponsored and partially supported by the European Union (EU) in the frame of the Cooperation in Science and Technology (COST) chemistry actions.