The author presents in detail a new non-perturbative approach to the fermionic many-body problem, improving the bosonization technique and generalizing it to dimensions d>1 via functional integration and Hubbard--Stratonovich transformations. In Part I he clearly illustrates the approximations and limitations inherent in higher-dimensional bosonization and derives the precise relation with diagrammatic perturbation theory. He shows how the non-linear terms in the energy dispersion can be systematically included into bosonization in arbitrary d, so that in d>1 the curvature of the Fermi surface can be taken into account. Part II gives applications to problems of physical interest, such as coupled metallic chains, electron-phonon interactions, disordered electrons, and electrons coupled to transverse gauge fields. The book addresses researchers and graduate students in theoretical condensed matter physics.

Development of the formalism.- Fermions and the Fermi surface.- Hubbard-Stratonovich transformations.- Bosonization of the Hamiltonian and the density-density correlation function.- The single-particle Green's function.- Applications to physical systems.- Singular interactions (f q ? |q|?? ).- Quasi-one-dimensional metals.- Electron-phonon interactions.- Fermions in a stochastic medium.- Transverse gauge fields.