This work provides a review of the state-of-the-art in semigroups of linear and nonlinear operations and applications. In addition to short introductory course notes in the linear and nonlinear theories, many of the leading researchers in the field contributed articles which are notable for their expository emphasis. Application areas include reaction-diffusion systems, other parabolic problems, scattering theory, fluid dynamics, continuum mechanics and mathematical biology. There is much emphasis on existence results, regularity properties, asymptotics, and problems that are not well-posed in the usual sense. The text is suitable for graduate students and researchers interested in the applications of operator theory and functional analysis to differential equations. Researchers in mathematical physics and mathematical biology and control theory should benefit from the expository account of recent developments in semigroup theory motivated by the applications.
