Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type ¿ i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions. Taken together, the contributions to this volume represent a comprehensive overview of current problems and developments.

Numerical Methods.- Density Matrix Renormalization.- Quantum Monte Carlo Methods for Strongly Correlated Electron Systems.- Lagrangian, Functional Integral, Renormalization Group, Conformal and Bosonization Methods.- Renormalization Group Technique for Quasi-One-Dimensional Interacting Fermion Systems at Finite Temperature.- An Introduction to Bosonization.- Disordered Quantum Solids.- Functional Derivatives, Mean-Field, Self-Consistent Methods, Slave-Bosons, and Extensions.- Self-Consistent Many-Body Theory for Condensed Matter Systems.- Fermi and Non-Fermi Liquid Behavior of Quantum Impurity Models: A Diagrammatic Pseudo-Particle Approach.- Conserving Approximations vs. Two-Particle Self-Consistent Approach.