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Nonlinear physics has been growing at an astounding rate over the past two decades and has changed its character from a collection of exotic examples of nonstandard behaviour to an all-embracing scientific methodology. This practical hands-on guide provides an overview of the features of condensed matter systems. This book provides self-contained background material, however the centrepiece of the text is the chapter dealing with a systematic development of nonlinear field equations for many-body systems. In order to equip the reader with concrete skills in tackling nonlinear problems in physics, the authors analyse in great detail several important applications such as metamagnetism, superconductivity, the Hubbard Hamiltonian and the multi-electron atom to name a few. A separate mathematical chapter shows in an easy-to-follow manner how the various integrable nonlinear differential equations that arise in physics can be solved analytically. This book will serve as a compendium of facts and references related to the subject area of nonlinear condensed matter physics. In addition, it can be used as practical introduction into currently developed nonlinear research methods in theoretical physics in general.