  This paper introduces a theory of Thermodynamic Formalism for Iterated
Function Systems with Measures (IFSm). We study the spectral properties of the
Transfer and Markov operators associated to a IFSm. We introduce variational
formulations for the topological entropy of holonomic measures and the
topological pressure of IFSm given by a potential. A definition of equilibrium
state is then natural and we prove its existence for any continuous potential.
We show, in this setting, a uniqueness result for the equilibrium state
requiring only the G\^ateaux differentiability of the pressure functional.
