The book grew out of lectures given over a period of about 30 to 35 years on Asymptotic Methods in sta- tistics. Most current texts, except the monographs by Le Cam (Springer-Verlag 1986) and Strasser (1985) emphasize a theory based on maximum likelihood estimates while this text emphasizes approximation by Gaussian families of measures, as well as quadratic expansions of log likelihood. The book presents in a short form some of the main results acquired in the past twenty years in the field of asymptotic statistical inference. The methods can be used very widely. The basic theorems are presented at a level that should not disturb a beginning graduate student. The authors have attempted a unified approach, in a simple setting, to methods to be found only in papers or specialized books.