  We present a new analytical approach to the strong electrostatic coupling
regime (SC), that can be achieved equivalently at low temperatures, high
charges, low dielectric permittivity etc. Two geometries are analyzed in
detail: one charged wall first, and then, two parallel walls at small
distances, that can be likely or oppositely charged. In all cases, one type of
mobile counter-ions only is present, and ensures electroneutrality (salt free
case). The method is based on a systematic expansion around the ground state
formed by the two-dimensional Wigner crystal(s) of counter-ions at the
plate(s). The leading SC order stems from a single-particle theory, and
coincides with the virial SC approach that has been much studied in the last 10
years. The first correction has the functional form of the virial SC
prediction, but the prefactor is different. The present theory is free of
divergences and the obtained results, both for symmetrically and asymmetrically
charged plates, are in excellent agreement with available data of Monte-Carlo
simulations under strong and intermediate Coulombic couplings. All results
obtained represent relevant improvements over the virial SC estimates. The
present SC theory starting from the Wigner crystal and therefore coined Wigner
SC, sheds light on anomalous phenomena like the counter-ion mediated
like-charge attraction, and the opposite-charge repulsion.
