Differential equations with impulses model processes subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve brief perturbations from continuous dynamics, where the duration of the perturbations is negligible compared to the overall evolution. Consequently, impulsive differential equations have been developed to address impulsive problems in various fields, including physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, and optimal control. Additionally, many studies in biology and medicine utilize these equations effectively. Over the past decade, the authors have made significant contributions to the literature on impulsive differential inclusions using fixed point methods. This work aims to consolidate their findings alongside those of other researchers related to their studies. The text explores the existence and stability of solutions for various initial value problems concerning impulsive differential equations and inclusions, addressing both fixed and variable moments, as well as boundary value problems. Since differential equations can be seen as specific cases of differential inclusions, the authors also delve into related questions regarding differential equations. This monograph covers a range of side issues stemming from its foundational concepts.
