This is one of two volumes which together comprise about 40 papers coming from the most outstanding contributions to the fourth European Quantum Systems in Chemistry and Physics workshop held in Marly, France, in 1999. These books cover a broad spectrum of scientific research work from quantum-mechanical many-body methods to important applications and computational developments, and from atoms and molecules to condensed matter. The first volume is subtitled "Basic Problems and Model Systems", which includes the following topics: density matrices and density functionals, electron correlation effects, relativistic formulations and effects, valence theory and nuclear motion. The second volume is subtitled "Advanced Problems and Complex Systems" and covers the following topics: response theory, reactive collisions and chemical reactions and condensed matter.