A new formalism is developed for the study of 3D and 2D sigma-models coupled to gravity which arise as result of the toroidal compactification of low-energy limit of the bosonic sector of heterotic string theory. This formalism is the natural matrix generalization of the well-known formalism of the Ernst potentials and related structures from Einstein-Maxwell theory to the field of the string gravity system under consideration. It turned out that an application of the new formalism was especially effective in the study of group of hidden symmetries of the theory and in the problems related to generation of new classes of its exact solutions using these symmetries. For example, it was succeeded in the finding of explicit form of general finite transformation of the three-dimensional charging symmetry subgroup and in the developing of the most general technique of generation of three-dimensional asymptotically flat solutions. The two-dimensional charging symmetries can be found in the framework of solution of inverse scattering transform problem, whereas the corresponding null-curvature representation of the theory is also one of the elements of the new formalism established. In particular, it becomes possible to write down the general class of asymptotically flat soliton solutions which possess an infinithesimal limit of the Geroch algebra form. This review is devoted to expound the general results mentioned and to illustrate them using the corresponding examples.

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