This volume is the second edition of a work that presents a coherent introduction to the subject of asymptotic statistics as it has developed in the past 50 years. The second edition differs from the first in that it has been made more 'reader friendly'. It also includes a new chapter, Chapter 4, on Gaussian and Poisson experiments because of their growing role in the field, especially in nonparametrics and semi-parametrics. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been ampliefied. Much of the material has been taught in a second year graduate course at Berkeley for 30 years. It represents a link between traditional material including maximum likelihood, and Wald's Theory of Statistical Decision Functions together with comparison and distances for experiments. This volume is not intended to replace monographs on specialized subjects, but it will help to place them in a coherent perspective. Lucien Le Cam is Professor of Statistics and Mathematics (Emeritus) at the University of California, Berkeley. He is the author of numerous papers on asymptotics and Asymptotic Methods in Statistical Decision Theory, Springer Verlag (1986). He was co-editor, with J. Neyman and E. Scott of the Berkeley Symposia on Mathematical Statistics and Probability. Grace Lo Yang is Professor, Department of Mathematics, University of Maryland, College Park. She is a long time holder of a Faculty Appointment at the National Institute of Standards and Technology, Gaithersburg, MD. Her research activities include stochastic modeling in physical sciences and theory of incomplete data.