This book, "Differential Inclusions" by Jean-Pierre Aubin and Arrigo Cellina, is part of the "Grundlehren der mathematischen Wissenschaften" series. It explores the theory and applications of differential inclusions, which are sets of possible velocities for a system, as opposed to the traditional differential equations where the velocity is uniquely determined by the state of the system. The authors discuss the motivations behind studying differential inclusions, including their relevance in various fields such as economics, social sciences, and biology. The book is divided into several chapters, covering topics such as set-valued maps, existence of solutions to differential inclusions, and the properties of trajectories. It also delves into optimal control theory and viability theory, which are crucial for selecting specific trajectories that satisfy given constraints. The authors provide applications of these theories, particularly in the context of economic systems, and discuss the use of feedback controls for regulating systems. The book is dedicated to the authors' families and acknowledges the support of various institutions and colleagues who contributed to its completion. It includes a comprehensive table of contents and references, making it a valuable resource for researchers and students in mathematics, economics, and related fields.This book, "Differential Inclusions" by Jean-Pierre Aubin and Arrigo Cellina, is part of the "Grundlehren der mathematischen Wissenschaften" series. It explores the theory and applications of differential inclusions, which are sets of possible velocities for a system, as opposed to the traditional differential equations where the velocity is uniquely determined by the state of the system. The authors discuss the motivations behind studying differential inclusions, including their relevance in various fields such as economics, social sciences, and biology. The book is divided into several chapters, covering topics such as set-valued maps, existence of solutions to differential inclusions, and the properties of trajectories. It also delves into optimal control theory and viability theory, which are crucial for selecting specific trajectories that satisfy given constraints. The authors provide applications of these theories, particularly in the context of economic systems, and discuss the use of feedback controls for regulating systems. The book is dedicated to the authors' families and acknowledges the support of various institutions and colleagues who contributed to its completion. It includes a comprehensive table of contents and references, making it a valuable resource for researchers and students in mathematics, economics, and related fields.