The book "Nonsmooth Analysis and Control Theory" is a graduate-level text that introduces the theory of nonsmooth analysis and its applications in control theory. It is part of the Graduate Texts in Mathematics series and is edited by F.H. Clarke, Yu.S. Ledyaev, R.J. Stern, and P.R. Wolenski. The book is designed for readers with a background in functional analysis and provides a clear and concise overview of nonsmooth analysis, which deals with differential analysis in the absence of differentiability. It covers topics such as proximal analysis, generalized gradients, and control theory, with a focus on applications in optimization, mechanics, and differential equations. The text is structured into chapters that introduce key concepts and theories, including proximal calculus in Hilbert spaces, generalized gradients in Banach spaces, and special topics in optimization and control theory. It includes numerous exercises and problems to help readers understand the material, as well as a detailed discussion of the relationship between different approaches to nonsmooth analysis. The book also provides a self-contained introduction to control theory, covering topics such as differential inclusions, invariance, viability, and viscosity solutions. The authors emphasize the importance of nonsmooth analysis in various areas of mathematics and engineering, and they argue that its methods and constructs will become an essential part of differential analysis in the future. The book is written in a way that is accessible to a wide audience, with a focus on clarity and conciseness. It includes a comprehensive list of references, a glossary of symbols, and a detailed index to aid in navigation. The book is intended for graduate students and researchers in mathematics, engineering, and related fields.The book "Nonsmooth Analysis and Control Theory" is a graduate-level text that introduces the theory of nonsmooth analysis and its applications in control theory. It is part of the Graduate Texts in Mathematics series and is edited by F.H. Clarke, Yu.S. Ledyaev, R.J. Stern, and P.R. Wolenski. The book is designed for readers with a background in functional analysis and provides a clear and concise overview of nonsmooth analysis, which deals with differential analysis in the absence of differentiability. It covers topics such as proximal analysis, generalized gradients, and control theory, with a focus on applications in optimization, mechanics, and differential equations. The text is structured into chapters that introduce key concepts and theories, including proximal calculus in Hilbert spaces, generalized gradients in Banach spaces, and special topics in optimization and control theory. It includes numerous exercises and problems to help readers understand the material, as well as a detailed discussion of the relationship between different approaches to nonsmooth analysis. The book also provides a self-contained introduction to control theory, covering topics such as differential inclusions, invariance, viability, and viscosity solutions. The authors emphasize the importance of nonsmooth analysis in various areas of mathematics and engineering, and they argue that its methods and constructs will become an essential part of differential analysis in the future. The book is written in a way that is accessible to a wide audience, with a focus on clarity and conciseness. It includes a comprehensive list of references, a glossary of symbols, and a detailed index to aid in navigation. The book is intended for graduate students and researchers in mathematics, engineering, and related fields.