Three-dimensional homogeneous spaces, not admitting invariant connections

The purpose of the work is the classification of three-dimensional isotropy-faithful homogeneous spaces, not admitting invariant connections. The local classification of homogeneous spaces is equivalent to the description of effective pairs of Lie algebras. If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariant connections. The peculiarity of techniques presented in the work is the application of purely algebraic approach, the compound of different methods of differential geometry, theory of Lie groups, Lie algebras and homogeneous spaces.