The description of solids at a microscopic level is complex,
involving the interaction of a huge number of its constituents, such as
ions or electrons. It is impossible to solve the corresponding
many-body problems analytically or numerically, although much insight
can be gained from the analysis of simplified models. An important
example is the Hubbard model, which describes interacting electrons in
narrow energy bands, and which has been applied to problems as diverse
as high-Tc superconductivity, band magnetism, and the metal-insulator
transition. This book presents a coherent, self-contained account of
the exact solution of the Hubbard model in one dimension. The early
chapters will be accessible to beginning graduate students with a basic
knowledge of quantum mechanics and statistical mechanics. The later
chapters address more advanced topics, and are intended as a guide for
researchers to some of the more recent scientific results in the field
of integrable models.