This book is intended to give a survey of relevant facts from functional analysis, positivity theory, and theory of semigroups, presented at a not too abstract but also not too superficial level, together with many proofs which are often difficult to find in literature. On the other hand, we discuss examples coming from the applied sciences, from population theory, through fragmentation processes, to various aspects of linear transport theory, emphasise the difference between the original model and its functional analytic reformulation, which makes it tractable by techniques introduced in the first part, and explore consequences of this dichotomy.
