Goodness of fit describes the validity of models involving statistical distribution of data, and smooth tests are a subset of these tests which are easy to apply and can be used in any situation in which there are relatively large sample sizes. Both concepts have become increasingly important with the advent of high-speed computers and the implementation of more complex models in the areas of probability and statistics. Written to be accessible to undergraduates with a working knowledge of statistics and calculus, this is an introductory reference work that should appeal to all professionals involved in statistical modelling.