Abstract. The estimations of the sectional curvature, one-dimensional curvature and the Ricci curvature on three dimensional Lie groups with left invariant Riemannian metrics are given in this paper. Becides this the Skhouten-Weil tensor and conformal flat one-parameter subgroups of three dimensional Lie groups with left invariant Riemannian metrics are investigated. For the proof of general theorems of this paper some formulas of J.Milnor's paper \cite{Miln} are used. The results of this paper are intersected with the results of D.Alekseevskii-B.Kimelfeld on a classification of conformal flat homogeneous Riemannian manifolds \cite{Alek} and the results of O.Kowalski-S.Nikcevic on Ricci eigenvalues of locally homogeneous Riemann 3-manifolds \cite{KN}.
AMSclassification. 53C20, 53C30
Keywords. Lie groups, curvature, left invariant Riemannian metrics