This textbook for a graduate level introductory course on data smoothing covers series estimators, kernel estimators, smoothing splines, and least-squares splines. The new edition deletes most of the asymptotic theory for smoothing splines and smoothing spline variants, and adds order selection for hierarchical models, estimation in partially linear models, polynomial-trigonometric regression, new results on bandwidth selection, and locally linear regression. The first edition was published as (1988).