  In this paper we present the Koopman-von Neumann (KvN) formulation of
classical non-Abelian gauge field theories. In particular we shall explore the
functional (or classical path integral) counterpart of the KvN method. In the
quantum path integral quantization of Yang-Mills theories concepts like
gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We
will prove that these same objects are needed also in this classical path
integral formulation for Yang-Mills theories. We shall also explore the
classical path integral counterpart of the BFV formalism and build all the
associated universal and gauge charges. These last are quite different from the
analog quantum ones and we shall show the relation between the two. This paper
lays the foundation of this formalism which, due to the many auxiliary fields
present, is rather heavy. Applications to specific topics outlined in the paper
will appear in later publications.
