The aim of this book is to develop an understanding and treatment of the problems of inference associated with experiments in science. Many textbooks treat inference as principally the reduction of the sample information to estimates and their marginal distribution and supposedly optimal properties. In contrast, this book emphasizes techniques for dividing the sample information into various parts addressing the diverse problems of inference that arise from repeatable experiments. An unusually valuable feature of the book is the large number of practical examples, many of which use data taken from experiments published in various scientific journals. This book has evolved from the author's courses on statistical inference. It would be a suitable text book for advanced undergraduate, Masters, and Ph.D. statistics students. It can also be used as a reference book. A background knowledge of an introductory course in probability is assumed, including the calculation and manipulation of probability functions and density functions, transformation of variables and the use of Jacobians. The author is a Distinguished Professor Emeritus of Statistics, University of Waterloo, and Professor of Statistics, Centro de Investigaci=F3n en Matemáticas, Guanajuato, Mexico. He is an Honorary member of the Statistical Society of Canada and a recipient of the Society's Gold Medal for Research. He is also an elected member of the International Statistical Institute and a Fellow of the American Statistical Association, of the Institute of Mathematical Statistics, and of the Royal Society of Canada.