The quantitative success that quantum chemistry has had since the early-1970s has led to the launch of "Conceptual Trends in Quantum Chemistry", a collection of essays intended to stimulate discussion in this field, of which the first volume was published in 1994, and the second in 1995. This third volume contains 14 papers covering topics such as recent developments in multiple scattering theory and density functional theory for molecules and solids; localized atomic hybrids; quantum electrodynamics and molecular structure; aspects of the chemical bond; Lie symmetries in quantum mechanics; the interplay between quantum chemistry and molecular dynamics simulations; the permutation group in many-electron theory; new developments in many body perturbation theory and coupled cluster theory; a philosopher's perspective of the "problem" of molecular shape; Van Der Waals interactions from density functional theories; different legacies and common aims; potential energy hypersurfaces for hydrogen bonded clusters (HF)N; one-electron pictures of electronic structure; and shape in quantum chemistry. This text should be of interest to researchers and graduate students whose work involves quantum chemistry, quantum mechanics, chemical physics, methodology, and mathematical statistical methods.