  A unified framework for theories of modified gravity will be an essential
tool for interpreting the forthcoming deluge of cosmological data. We present
such a formalism, the Parameterized Post-Friedmann framework (PPF), which
parameterizes the cosmological perturbation theory of a wide variety of
modified gravity models. PPF is able to handle spin-0 degrees of freedom from
new scalar, vector and tensor fields, meaning that it is not restricted to
simple models based solely on cosmological scalar fields. A direct
correspondence is maintained between the parameterization and the underlying
space of theories, which allows us to build up a `dictionary' of modified
gravity theories and their PPF correspondences. In this paper we describe the
construction of the parameterization and demonstrate its use through a number
of worked examples relevant to the current literature. We indicate how the
formalism will be implemented numerically, so that the dictionary of modified
gravity can be pitted against forthcoming observations.
