This chapter discusses the elementary statistical properties of the kernel estimator in the univariate case. The method is of wide applicability, particularly in the univariate case, and it is certainly worth understanding its behaviour before going on to consider other methods. The development will include both theoretical and practical aspects of the method, but, generally, only that theory of reasonably immediate practical relevance will be included. There are many practical problems where the assumptions are not necessarily justifiable, but nevertheless they provide a standard framework in which to discuss the properties of density estimation methods. The problem of choosing how much to smooth is of crucial importance in density estimation. Before discussing various methods in detail, it is worth pausing to make some remarks of a general nature. A natural method for choosing the smoothing parameter is to plot out several curves and choose the estimate that is most in accordance with one's prior ideas about the density.