Entropy and Information Theory is a comprehensive textbook that explores the mathematical foundations of information theory, focusing on probabilistic information measures and their applications to coding theorems for information sources and noisy channels. The book emphasizes source coding and stationary codes, aiming to develop Shannon's mathematical theory of communication for single-user systems. It provides a detailed treatment of key concepts such as entropy, mutual information, conditional entropy, and relative entropy, along with their limiting versions like entropy rate and information rate. The text also addresses the distance or distortion between random objects, focusing on the accuracy of representation and mutual approximation. It combines information convergence results with ergodic theorems to prove general Shannon coding theorems for sources and channels. The book is influenced by the works of Pinsker, Kolmogorov, Gelfand, Yaglom, and Dobrushin, and it extends Shannon's original results. The mathematical models used are more general than traditional treatments, considering nonstationary and nonergodic information processes. The book also explores various code structures, including block codes, stationary codes, and sliding-block codes, and their relationships. It includes new chapters on the interplay between distortion and entropy, distortion and information, and properties of good source codes. The book is self-contained, with some results found in a previous work. It is intended for engineers and mathematicians, providing insights into mathematical aspects and engineering applications of information theory. The second edition includes corrections, rearrangements, and new material, expanding discussions and including recent results. The book covers topics such as entropy, information rates, distortion and approximation, source coding theorems, and coding for noisy channels. It also discusses ergodic theory, information theory, and their applications, including the Ornstein isomorphism theorem and the development of coding techniques for communication systems. The book is structured into chapters covering various aspects of information theory, including entropy, distortion, source coding, and channel coding, with a focus on the mathematical foundations and practical applications of information theory.Entropy and Information Theory is a comprehensive textbook that explores the mathematical foundations of information theory, focusing on probabilistic information measures and their applications to coding theorems for information sources and noisy channels. The book emphasizes source coding and stationary codes, aiming to develop Shannon's mathematical theory of communication for single-user systems. It provides a detailed treatment of key concepts such as entropy, mutual information, conditional entropy, and relative entropy, along with their limiting versions like entropy rate and information rate. The text also addresses the distance or distortion between random objects, focusing on the accuracy of representation and mutual approximation. It combines information convergence results with ergodic theorems to prove general Shannon coding theorems for sources and channels. The book is influenced by the works of Pinsker, Kolmogorov, Gelfand, Yaglom, and Dobrushin, and it extends Shannon's original results. The mathematical models used are more general than traditional treatments, considering nonstationary and nonergodic information processes. The book also explores various code structures, including block codes, stationary codes, and sliding-block codes, and their relationships. It includes new chapters on the interplay between distortion and entropy, distortion and information, and properties of good source codes. The book is self-contained, with some results found in a previous work. It is intended for engineers and mathematicians, providing insights into mathematical aspects and engineering applications of information theory. The second edition includes corrections, rearrangements, and new material, expanding discussions and including recent results. The book covers topics such as entropy, information rates, distortion and approximation, source coding theorems, and coding for noisy channels. It also discusses ergodic theory, information theory, and their applications, including the Ornstein isomorphism theorem and the development of coding techniques for communication systems. The book is structured into chapters covering various aspects of information theory, including entropy, distortion, source coding, and channel coding, with a focus on the mathematical foundations and practical applications of information theory.