A system using Transverse Mercator projections to map the world into numerous standard zones that are six degrees wide. The standard Manifold Gauss-Kruger projection is also known as the Pulkovo 1942 Gauss-Kruger projection. A similar Gauss-Kruger projection is implemented as a national grids projection for Germany under the names Germany Gauss-Kruger Zone n (DHDN) with n from 1 to 5 for Zone 1 through Zone 5.
Americans can best understand the Gauss Kruger system by thinking of it as a version of the Universal Transverse Mercator (UTM) system with zones defined for European and Asian coverage. (Europeans, of course, can think of the UTM system as a version of the Gauss Kruger system that has been implemented by Americans.)
See the Universal Transverse Mercator projection topic for information on how systems such as UTM and Gauss Kruger operate. See the Transverse Mercator projection topic for a note on Carl Friedrich Gauss.
Like UTM or the State Plane Coordinate System, the Gauss Kruger system of projections is a living fossil. It was created mostly as a reflection of the technological limitations of an earlier era. When used with skill as originally intended it continues to function well in expert hands. The problem with the Gauss Kruger system (as with UTM or the State Plane) is that it is frequently misused by inexpert users who do not realize the limitations built into the system.