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Screening of a macroion such as a charged solid particle, a charged membrane,double helix DNA or actin by multivalent counterions is considered. Smallcolloidal particles, charged micelles, short or long polyelectrolytes can playthe role of multivalent counterions. Due to strong lateral repulsion at thesurface of macroion such multivalent counterions form a strongly correlatedliquid, with the short range order resembling that of a Wigner crystal. Thesecorrelations create additional binding of multivalent counterions to themacroion surface with binding energy larger than $k_BT$. As a result even for amoderate concentration of multivalent counterions in the solution, their totalcharge at the surface of macroion exceeds the bare macroion charge in absolutevalue. Therefore, the net charge of the macroion inverts its sign. In thepresence of a high concentration of monovalent salt the absolute value ofinverted charge can be larger than the bare one. This giant inversion of chargecan be observed by electrophoresis or by direct counting of multivalentcounterions.Comment: 17 pages, 9 figures. Many corrections. Accepted to J. Chem. Phy

Screening of a charged particle by multivalent counterions in salty water: Strong charge inversion