An exact statistical mechanical theory for fluid mixtures of rigid molecules with arbitrary charge distributions, sizes, and shapes is presented. It deals with many-body effects in electrostatic interactions between molecules in fluids and can, for example, be applied to mixtures of polar molecules and to solutions of electrolytes or colloidal dispersions in polar molecular solvents. All solute and solvent molecules are treated on the same fundamental level in statistical mechanics. The exact screened Coulomb potential phi(0)(r) for the solution is given a general definition. A renormalized charge distribution rho(i)(0) for each molecule of any species i is uniquely defined such that the total electrostatic potential from each i molecule is exactly given by phi(0) with rho(i)(0) as the source. By using rho(i)(0) when calculating the interaction between the molecule and the total electrostatic potential from any source, one includes the indirect effects from the surrounding polarizable molecular medium on the electrostatic part of the potential of mean force for the molecule. In general, all kinds of molecules (charged, polar, and apolar ones) acquire renormalized charges in electrolyte solutions. The dielectric function and other fundamental properties of the mixture can be expressed in terms of rho(i)(0) for all species. The formally exact theory is expressed in a Poisson-Boltzmann (PB)-type manner by using the renormalized rather than actual (bare) charges and it is shown that the total electrostatic potential due to a molecule satisfies an equation that is the exact version of the linear PB equation. The decay behaviors of phi(0), the pair potential of mean force and pair distribution functions are investigated. (C) 2003 American Institute of Physics.