We aim to build an extensive class of statistical models by combining a small number of basic statistical ideas in diverse ways. Although we use (a very small part of) mathematics as our basic tool to describe the statistics, our aim is not primarily to develop theorems and proofs of theorems, but rather to provide the statistician with statistical tools for dealing with inferences from a wide range of data, which may be structured in many different ways. We develop an extended likelihood framework, derived from classical likelihood, which is itself described in Chapter 1.