The main part of this book is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and bound-level information. The bound-level treatment gives a clear physical understanding of "difficult" questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.

Zusammenfassung
In this third edition the book has been expanded in three directions: 1. Problems have been added at the end of each chapter (40% of which are solved in the last section of the book) together with suggestions for further reading. Furthermore, the number of appendices (marked with a grey stripe) has been substantially enlarged in order to make the book more self-su?cient. These additions, together with many clari?cations in the text, render the book more suitable as a companion in a course on Greens functions and their applications. 2. Theimpressivedevelopmentsofthe1980sand1990sinmesoscopicphysics, and in particular in transport properties, found their way to a c- tain extent in the new Chaps.8 and 9 (which also contain some of the material of the old Chap.7). This is a natural expansion, since Greens functions have played an important role as a theoretical tool in this new ?eld of physics, a role that continues in nanoregime research (see, e.g., recent publications dealing with carbon nanotubes). Thus, the powerful and unifying formalism of Greens functions ?nds applications not only in standard physics subjects such as perturbation and scattering theory, bound-state formation, etc., but also at the forefrontof current and, most likely, future developments. 3. Over the last 15 yearsor so Greens functions havefound applications not only in condensed matter electronicmotion but in classicalwavepropa- tion in both periodic and random media; photonic and phononic crystals aretheoutcomesofthislineofresearchwhoseunderlyingbasictheoretical principles are summarized in Sect.7.2.4.

Inhalt
Green's Functions in Mathematical Physics.- Time-Independent Green's Functions.- Time-Dependent Green's Functions.- Green's Functions in One-Body Quantum Problems.- Physical Significance of G. Application to the Free-Particle Case.- Green's Functions and Perturbation Theory.- Green's Functions for Tight-Binding Hamiltonians.- Single Impurity Scattering.- Two or More Impurities; Disordered Systems.- Electrical Conductivity and Green's Functions.- Localization, Transport, and Green's Functions.- Green's Functions in Many-Body Systems.- Definitions.- Properties and Use of the Green's Functions.- Calculational Methods for g.- Applications.