Advances in the Theory of Quantum Systems in Chemistry and Physics is a collection of 32 selected papers from the scientific contributions presented at the 15th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XV), held at Magdalene College, Cambridge, UK, from August 31st to September 5th, 2010. This volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a wide range of problems in chemistry, physics, and biology. The breadth and depth of the scientific topics discussed during QSCP-XV are gathered in seven sections: I. Fundamental Theory; II. Model Atoms; III. Atoms and Molecules with Exponential-Type Orbitals; IV. Density-Oriented Methods; V. Dynamics and Quantum Monte-Carlo Methodology; VI. Structure and Reactivity; VII. Complex Systems, Solids, Biophysics. Advances in the Theory of Quantum Systems in Chemistry and Physics is written for research students and professionals in Quantum systems of chemistry and physics. It also constitutes and invaluable guide for those wishing to familiarize themselves with research perspectives in the domain of quantum systems for thematic conversion or simply to gain insight into the methodological developments and applications to physics chemistry and biology that have actually become feasible by the end of 2010.