Statistics is the science that focuses on drawing conclusions from data, by analyzing and modeling the data using probabilistic models. In An Introduction to Mathematical Statistics (PDF) the author describes key concepts from statistics and give a mathematical basis for important statistical methods. Much attention is paid to the sound application of those methods to data. The 3 main topics in statistics are tests, confidence regions and estimators. The authors illustrate these in many good examples, with a separate chapter on regression models, including analysis of variance and linear regression. They also discuss the optimality of estimators and tests, as well as the selection of the best-fitting models. Every chapter ends with a case study in which the described statistical methods are applied. This ebook assumes a basic knowledge of calculus, linear algebra and probability theory.