On account of Lieb and Wu's 1968 Bethe ansatz solution, the one-dimensional Hubbard model has become a laboratory for theoretical studies of non-perturbative effects in strongly correlated electron systems. Many of the tools available for the analysis of such systems have been applied to this model, both to provide complementary insights to what is known from the exact solution or as an ultimate test of their quality. In parallel, due to the synthesis of new quasi one-dimensional materials and the refinement of experimental techniques, the one-dimensional Hubbard model has evolved from a toy model to a paradigm of experimental relevance for strongly correlated electron systems.

Due to the ongoing efforts to improve our understanding of one-dimensional correlated electron systems, there exists a large number of review articles and books covering various aspects of the general theory, as well as the Bethe ansatz and field theoretical methods. A collection of these works is listed in the General Bibliography below.

Still we felt – and many of our colleagues shared this view – that there would be a need for a coherent account of all of these aspects in a unified framework and from the perspective of the one-dimensional Hubbard model, which, moreover, would be accessible to beginners in the field. This motivated us to write this volume. It is intended to serve both as a textbook and as a monograph.