This book is intended for use in a rigorous introductory Ph.D.-level course in econometrics, or in a field course in econometric theory. It covers the measure - theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory.