This book constitutes the first effort to summarize a large volume of results obtained over the
past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical
settings that it describes. It contains an introduction to the model its systematic derivation
and its connection to applications a subsequent analysis of the existence and the stability of
fundamental nonlinear structures in 1 2 and even 3 spatial lattice dimensions. It also covers
the case of defocusing nonlinearities the modulational instabilities of plane wave solutions
and the extension to multi-component lattices. In addition it features a final chapter on
special topics written by a wide array of experts in the field addressing through short
reviews areas of particular recent interest.
