Separation of signal from noise is the most fundamental problem in data analysis, and arises in many fields, for example, signal processing, econometrics, acturial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, and extensions to local likelihood and density estimation. Basic theoretical results and diagnostic tools such as cross validation are introduced along the way. Examples illustrate the implementation of the methods using the LOCFIT software.