Preface.- List of Symbols.- 1 Prerequisites from Probability Theory.- 2 A Poisson Limit Theorem for Triangular Arrays .- 3 The Method of Moments .- 4 A Central Limit Theorem for Stationary m-Dependent Sequences.- 5 The multivariate normal distribution .- 6 Convergence in Distribution and Central Limit Theorem in R^d .- 7 Empirical Distribution Function.- 8 Limit Theorems for U-Statistics.- 9 Basic Concepts of Estimation Theory.- 10 Maximum Likelihood Estimation.- 11 Asymptotic (relative) efficiency of estimators.- 12 Likelihood Ratio Tests.- 13 Probability Measures on Metric Spaces.- 14 Convergence of Distributions in Metric Spaces.- 15 Wiener Process, Donsker's Theorem, and Brownian Bridge.- 16 The Space D[0,1], Empirical Processes.- 17 Random Elements in Separable Hilbert Spaces.- Afterword.- Solutions to the Problems.- Bibliography.- Index.