In my original proposal to Springer for a book on Quantal Density Functional Theory, I had envisaged one that was as complete in its presentation as possible, describing the basic theory as well as the approximation methods and a host of applications. However,after workingon the bookforabout ?ve years, I realizedthat the goal was too ambitious, and that I would be writing for another ?ve years for it to be achieved. Fortunately,there was a natural breakin the material, and I proposed to my editor, Dr. Claus Ascheron, that we split the book into two components: the ?rst on the basic theoretical framework, and the second on approximation methods and applications. Dr. Ascheron consented, and I am thankful to him for agreeing to do so. Hence, we published Quantal Density Functional Theory in 2004, and are now publishing Quantal Density Functional Theory II: Approximation Methods and Applications. One signi?cant advantage of this, as it turns out, is that I have been able to incorporate in each volume the most recent understandings available. This volume, like the earlier one, is aimed at advanced undergraduates in physics and chemistry, graduate students and researchers in the ?eld. It is written in the same pedagogical style with details of all proofs and numerous ?gures provided to explain the physics. The book is independent of the ?rst volume and stands on its own. However, proofs given in the ?rst volume are not repeated here.

Schr#x00F6;dinger Theory from a #x201C;Newtonian#x201D; Perspective.- Quantal Density Functional Theory.- New Perspectives on Hohenberg#x2013;Kohn#x2013;Sham Density Functional Theory.- Nonuniqueness of the Effective Potential Energy and Wave Function in Quantal Density Functional Theory.- Approximations Within Quantal Density Functional Theory.- Analytical Asymptotic Structure in the Classically Forbidden Region of Atoms.- Analytical Asymptotic Structure At and Near the Nucleus of Atoms.- Application of the Q-DFT Hartree Uncorrelated Approximation to Atoms.- Application of the Q-DFT Pauli Correlated Approximation to Atoms and Negative Ions.- Quantal Density Functional Theory of the Density Amplitude: Application to Atoms.- Application of the Irrotational Component Approximation to Nonspherical Density Atoms.- Application of Q-DFT to Atoms in Excited States.- Application of the Multi-Component Q-DFT Pauli Approximation to the Anion#x2013;Positron Complex: Energies, Positron and Positronium Affinities.- Application of the Q-DFT Fully Correlated Approximation to the Helium Atom.- Application of the Q-DFT Fully Correlated Approximation to the Hydrogen Molecule.- Application of Q-DFT to the Metal#x2013;Vacuum Interface.- Many-Body and Pseudo M#x00F8;ller-Plesset Perturbation Theory within Quantal Density Functional Theory.- Epilogue.