This book is a research monograph in the relatively new field of nonparametric regression. It serves as an introduction to the field for graduate students, researchers and statistical consultants in statistics and biostatistics, but is also intended as an overview over some recent research developments in the fixed design case. Basic ideas are developed for various nonparametric curve estimators. The emphasis is on kernel estimators as a unifying concept and on the interplay between theory and practical application. Problems of practical application are illustrated in several examples of analyses of longitudinal medical data sets. These demonstrate the need of including nonparametric regression in addition to the classical parametric regression into the repertoire of practicing statisticians/biostatisticians. One goal of the book is to stimulate the reader to experiment with the methods and to gain experience by applying them. This is facilitated by an Appendix containing several relevant FORTRAN programs.