Quantum mechanics was still in swaddling clothes when Thomas, Fermi, Dirac and von Weizsacker initiated the line of thought from which this work derives. Its current vitality owes much to a result achieved by Hohenberg and Kohn (who supplies the foreword) in 1964. The monograph provides advanced graduate students and many-body physicists/chemists with careful review of the present state of a rich body of technique, the objective of which is to by-pass solution of the Schrodinger equation enroute to a fairly detailed description of the ground state properties of many body systems. Has the feel of a review article which outgrew the capacity of any journal (which, the authors inform us, was in fact its origin), and retains at least some of the attractive brevity of such a review, the whole done up in the familiar Springer style.