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This book is devoted to one of the central problems of Information Theory; the problem of determination of interdependence of coding rate and of error probability exponent for different information transmission systems. The overview deals with memoryless systems of finite alphabet setting. It briefly formulates fundamental notions and results of Shannon theory on reliable transmission via coding and gives a survey of results obtained in last two-three decades by the authors, their colleagues and other researchers. The book is written with the goal to make accessible to a broader circle of readers the concept of rate-reliability. This concept is useful to solve these problems as well as elaborating the idea of reliability-reliability dependence related to statistical hypothesis testing and identification. Reliability Criteria in Information Theory and Statistical Hypothesis Testing is ideal reading for students, researchers and professionals working in Information Theory.