Frontiers in Mathematics

This monograph serves two primary purposes. First, it provides a comprehensive treatment of bi-continuous semigroup theory and its applications, ranging from network theory to control theory. The exposition proceeds systematically from fundamental theory through approximation methods, extrapolation techniques as well as perturbation theory, concluding with applications to networks, mean ergodicity and control systems. Each chapter includes illustrative examples to reinforce the theoretical concepts.Second, this work aims at supporting emerging researchers and doctoral students by offering a structured foundation for further investigation in operator semigroups. By synthesizing current knowledge, it provides a reference point for new research projects in this domain.