The Mathematics of Computerized Tomography by F. Natterer is a comprehensive book that explores the mathematical foundations of computerized tomography (CT). CT refers to the reconstruction of a function from its line or plane integrals, and it has found applications in various fields, including diagnostic radiology. The book aims to provide a mathematical understanding of CT for both researchers and practitioners. It covers the theory and algorithms of CT, as well as the state of the art in the mathematical theory of CT since its introduction in the early 1970s. The book is self-contained, with a brief review of the necessary mathematical background in an appendix. It discusses the Radon transform and related transforms, sampling and resolution, ill-posedness and accuracy, reconstruction algorithms, incomplete data, and mathematical tools. The text is mathematically rigorous, but it also provides practical interpretations to help readers understand the relevance of the mathematical concepts. The book is based on courses given by the author at the Universities of Saarbrücken and Münster. It includes contributions from other scholars, such as D. C. Solomon and E. T. Quinto, who provided critical feedback and suggestions for improvement. The author also acknowledges the support of colleagues like A. Faridani, U. Heike, and H. Kruse, who helped in the completion of the book. The book covers essential parts of the theory of CT, which are now well understood. However, it omits some important aspects, such as the statistical side of CT, which is crucial in practice. The book is intended for a wide audience, including mathematicians and practitioners in various fields. It provides a thorough mathematical treatment of CT, making it an essential reference for those interested in the subject.The Mathematics of Computerized Tomography by F. Natterer is a comprehensive book that explores the mathematical foundations of computerized tomography (CT). CT refers to the reconstruction of a function from its line or plane integrals, and it has found applications in various fields, including diagnostic radiology. The book aims to provide a mathematical understanding of CT for both researchers and practitioners. It covers the theory and algorithms of CT, as well as the state of the art in the mathematical theory of CT since its introduction in the early 1970s. The book is self-contained, with a brief review of the necessary mathematical background in an appendix. It discusses the Radon transform and related transforms, sampling and resolution, ill-posedness and accuracy, reconstruction algorithms, incomplete data, and mathematical tools. The text is mathematically rigorous, but it also provides practical interpretations to help readers understand the relevance of the mathematical concepts. The book is based on courses given by the author at the Universities of Saarbrücken and Münster. It includes contributions from other scholars, such as D. C. Solomon and E. T. Quinto, who provided critical feedback and suggestions for improvement. The author also acknowledges the support of colleagues like A. Faridani, U. Heike, and H. Kruse, who helped in the completion of the book. The book covers essential parts of the theory of CT, which are now well understood. However, it omits some important aspects, such as the statistical side of CT, which is crucial in practice. The book is intended for a wide audience, including mathematicians and practitioners in various fields. It provides a thorough mathematical treatment of CT, making it an essential reference for those interested in the subject.