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Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book presents a survey of the results that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material. The second part then deals with the application of the developed theory to a variety of problems ranging from the classical birth-and-death type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models. The only prerequisites are a basic knowledge of functional analysis and measure theory. This is an essential one-stop reference for graduate and postgraduate students and researchers in applied analysis and mathematical physics who are interested in the application of functional analytic techniques to concrete problems arising in physics, biology and engineering.