Small-Sample Theory -- The General Decision Problem -- The Probability Background -- Uniformly Most Powerful Tests -- Unbiasedness: Theory and First Applications -- Unbiasedness: Applications to Normal Distributions; Confidence Intervals -- Invariance -- Linear Hypotheses -- The Minimax Principle -- Multiple Testing and Simultaneous Inference -- Conditional Inference -- Large-Sample Theory -- Basic Large Sample Theory -- Quadratic Mean Differentiable Families -- Large Sample Optimality -- Testing Goodness of Fit -- General Large Sample Methods. .The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760. E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands and the University of Chicago. He is the author of Elements of Large-Sample Theory and (with George Casella) he is also the author of Theory of Point Estimation, Second Edition. Joseph P. Romano is Professor of Statistics at Stanford University. He is a recipient of a Presidential Young Investigator Award and a Fellow of the Institute of Mathematical Statistics. He has coauthored two other books, Subsampling with Dimitris Politis and Michael Wolf, and Counterexamples in Probability and Statistics with Andrew Siegel. .