The purpose of the work is the classification of three-dimensional non-reductive homogeneous spacesnot admitting normal connections, affine connections, their torsion tensors, curvature and holonomy algebras.The object of investigation arepointed-non-reductive spaces and connections on them. The basic notions, such as the isotropically-faithful pair, reductive space, afne connection, curvature tensor and torsion tensor, holonomy algebra and normal connection are defined.
