Quantal Density Functional Theory II : Approximation Methods and Applications This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT) a new local effective potential energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle Coulomb repulsion and the correlation contribution to the kinetic energy the Correlation Kinetic effects are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations as well as a many body perturbation theory within the context of QDFT are developed. The applications are to the few electron inhomogeneous electron gas systems in atoms and molecules as well as to the many electron inhomogeneity at metallic surfaces.