We now breathe some life into the PPN formalism by presenting a chapter full of metric theories of gravity and their post-Newtonian limits. This chapter will illustrate an important application of the PPN formalism, that of comparing and classifying theories of gravity. We begin in Section 5.1 with a discussion of the general method of calculating post-Newtonian limits of metric theories of gravity. The theories to be discussed in this chapter are divided into three classes. The first class is that of purely dynamical theories (see Section 3.3). These include general relativity in Section 5.2; scalar–tensor theories, of which the Brans–Dicke theory is a special case in Section 5.3; and vector–tensor theories in Section 5.4. The second class is that of theories with prior geometry. These include bimetric theories in Section 5.5; and “stratified” theories in Section 5.6. The theories described in detail in these five sections are those of which we are aware that have a reasonable chance of agreeing with present solar system experiments, to be described in Chapters 7, 8, and 9. Table 5.1 presents the PPN parameter values for the theories described in these five sections. The third class of theories includes those that, while perhaps thought once to have been viable, are in serious violation of one or more solar system tests. These will be described briefly in Section 5.7.