This text has grown out of notes used for lectures in a course entitles Advanced Statistical Theory at Carnegie Mellon University over several years. The course (when taught by the author) has attempted to cover, in one academic year, those topics in estimation, testing, and large sample theory that are commonly taught to second year graduate students in a mathematically rigorous fashion. Most tests at this level fall into one of two categories. They either ignore the Bayesian point of view altogether or they cover Bayesian topics almost exclusively. This book covers topics in both classical and Bayesian inference in a great deal of generality. My own point of view is Bayesian, but I believe that students need to learn both types of theory in order to achieve a fuller appreciation of the subject matter. Although many comparisons are made between classical and Bayesian methods, it is not a goal of the text to present a formal comparison of the two approaches as was done by Barnnet (1982). Rather, the goal has been to prepare Ph.D. students to be able to understand and contribute to the literature of theoretical statistics with a broader perspective than would be achieved from a purely Bayesian or a purely classical course.