The book "Observation and Control for Operator Semigroups" by Marius Tucsnak and George Weiss is an advanced text in the field of operator semigroups, focusing on observability and controllability for infinite-dimensional systems. Edited by Herbert Amann, Steven G. Krantz, Shrawan Kumar, and Jan Nekovář, the book covers topics such as norms and inner products, operators on finite-dimensional spaces, matrix exponentials, and the Hautus test. It delves into strongly continuous semigroups, their generators, spectra, and resolvents, as well as invariant subspaces, Riesz bases, and diagonalizable operators. The authors also discuss semigroups of contractions, dissipative and m-dissipative operators, self-adjoint and positive operators, and the wave equation with boundary damping. The book includes detailed chapters on admissibility, observability, and controllability, with numerous examples from partial differential equations (PDEs) and worked-out solutions. It aims to provide an elementary introduction to these topics, assuming only a basic understanding of bounded operators on Hilbert spaces, differential equations, Fourier and Laplace transforms, distributions, and Sobolev spaces. The book is intended for researchers and students interested in the theory and applications of operator semigroups in control theory.The book "Observation and Control for Operator Semigroups" by Marius Tucsnak and George Weiss is an advanced text in the field of operator semigroups, focusing on observability and controllability for infinite-dimensional systems. Edited by Herbert Amann, Steven G. Krantz, Shrawan Kumar, and Jan Nekovář, the book covers topics such as norms and inner products, operators on finite-dimensional spaces, matrix exponentials, and the Hautus test. It delves into strongly continuous semigroups, their generators, spectra, and resolvents, as well as invariant subspaces, Riesz bases, and diagonalizable operators. The authors also discuss semigroups of contractions, dissipative and m-dissipative operators, self-adjoint and positive operators, and the wave equation with boundary damping. The book includes detailed chapters on admissibility, observability, and controllability, with numerous examples from partial differential equations (PDEs) and worked-out solutions. It aims to provide an elementary introduction to these topics, assuming only a basic understanding of bounded operators on Hilbert spaces, differential equations, Fourier and Laplace transforms, distributions, and Sobolev spaces. The book is intended for researchers and students interested in the theory and applications of operator semigroups in control theory.