\textit{O. Kowalski} and \textit{J. Szenthe} [Geom. Dedicata 81, 209--214 (2000; Zbl 0980.53061)] proved that every homogeneous Riemannian manifold admits at least one homogeneous geodesic. Consequently, it was quite natural to ask whether there exist more homogeneous geodesics. \textit{O.\ Kowalski, S. Nikčević} and \textit{Z. Vlášek} in another paper [Singapore: World Scientific, 104--112 (2000; Zbl 0989.53025)] asked the following two questions: (1) Let \(M=K/H\) be a homogeneous Riemannian manifold, where \(K\) is the largest connected group of isometries and \(\dim M\geq 3\). Does \(M\) always admit more than one homogeneous geodesic? (2) Suppose that \(M=K/H\) admits \(m=\dim M\) linearly independent homogeneous geodesics through the origin \(o\). Does it admit \(m\) mutually orthogonal homogeneous geodesics? They gave negative answers to both these questions by considering a three dimensional non-unimodular Lie group \(G=K/H\) endowed with a left invariant Riemannian metric \(g\) with distinct Ricci principal curvatures. The author of the paper under review studies systematically three dimensional Lie groups (without any restrictions) endowed with left invariant Riemannian metric (without any assumption on the principal Ricci curvatures) and clarifies completely the structure of the homogeneous geodesics.