This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2^nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the ¿quantal Newtonian¿ second and first laws for the individual electron. These laws are in terms of ¿classical¿ fields that pervade all space, and their quantal sources. Thefields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schrödinger theory from the new perspective of the single electron in terms of the ¿quantal Newtonian¿ laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.