This is a text divided into two volumes for a two-semester course in mathematical statistics at the senior/graduate level. The two main pedagogical aspects in these volumes are: (i) the material is designed in lessons (each for a 50-minute class) with complementary exercises and homework, and (ii) although the material is traditional, great care is taken to provide self-contained, rigorous, and complete presentations. An elementary introduction to characteristic functions and probability measures and integration, but not general measure theory in Volume I, allows for a complete proof of some central limit theorems and a rigorous treatment of the asymptotic properties of statistical inference. Students need to be familiar only with concepts such as Jacobians and eigenvalues of matrices. Volume II: Statistical Inference is designed for the second semester and contains a rigorous introduction to mathematical statistics.