We describe the general characteristics of metric theories of gravity, and review the equations of non-gravitational physics in curved spacetime. We introduce the Strong Equivalence Principle, which generalizes the Einstein Equivalence Principle to situations where local gravitational interactions are important, and discuss why general relativity may be unique in conforming to this principle.

We discuss tests of the Strong Equivalence Principle. We derive the observable consequences of the Nordtvedt effect, a violation of the equality of acceleration of massive, self-gravitating bodies, that occurs in many alternative theories of gravity, although not in general relativity. We discuss the bounds obtained on this effect via lunar laser ranging, and via measurements of pulsar-white dwarf binary systems. We derive a number of observable consequences of preferred-frame effects in binary orbits and in the structure of self-gravitating bodies, and review the bounds that have been placed on the relevant PPN parameters by a wide range of observations.

We derive the equations of motion for a variety of physical systems in the PPN formalism, including photons, fluid systems, and N-body systems consisting of well-separated self-gravitating objects. We also specialize to two-body systems and describe the framework for calculating perturbations of Keplerian orbit elements induced by post-Newtonian corrections in the equations of motion. For a class of theories based on an invariant action, we obtain the Lagrangian that describes the dynamics of an N-body system. We derive the locally-measured, or effective gravitational constant, as measured by a Cavendish experiment, within the PPN formalism. For spinning bodies, we obtain the equations of motion and the equations of spin precession.