  Multifractal analysis refers to the study of the local properties of measures
and functions, and consists of two parts: the fine multifractal theory and the
coarse multifractal theory. The fine and the coarse theory are linked by a web
of conjectures known collectively as the Multifractal Formalism. Very roughly
speaking the Multifractal Formalism says that the multifractal spectrum from
fine theory equals the Legendre transform of the Renyi dimensions from the
coarse theory.
  Recently {\it fine} multifractal zeta-functions, i.e. multifractal
zeta-functions designed to produce detailed information about the fine
multifractal theory, have been introduced and investigated. The purpose of this
work is to complement and expand this study by introducing and investigating
{\it coarse} multifractal zeta-functions, i.e. multifractal zeta-functions
designed to produce information about the coarse multifractal theory, and, in
particular, to establish a {\it Multifractal Fortmalism for Zeta-Functions}
linking fine multifractal zeta-functions and coarse multifractal zeta-functions
via the Legendre transform.
  Several applications are given, including applications to multifractal
analysis of graph-directed self-conformal measures and multifractal analysis of
ergodic Birkhoff averages of continuous functions on graph-directed
self-conformal sets.
