A microscopic statistical theory of polyelectrolyte solutions (PES) with polyions of low linear charge density is developed in the random phase approximation (RPA). Correlation functions of a multi-component PES and the fluctuational electrostatic contribution to the free energy of the system are calculated. Owing to the high-polymer nature of the system these expressions differ essentially from those of Debye-Huckel (DH) type. It is shown that under certain conditions a microphase separation into oppositely charged domains takes place in PES. The phase diagram is given. The expressions for the screened Coulomb potential of a test charge are obtained. In some cases the potential oscillates. The RPA is shown to be valid for intermediate monomer or salt concentrations and is violated at very low or very high concentrations.