These lecture notes cover the classification of three-dimensional complex manifolds on which a real Lie groups acts transitively by biholomorphic transformations. This classification was obtained in two steps. First, in the Diplomarbeit of the author, all those three-dimensional complex manifolds were classified on which a complex Lie group acts transitively. Later, in the Ph.D. thesis of the author, the classification was extended to cover all three-dimensional complex manifolds on which a real Lie group acts transitively. The lecture notes cover both the work done in the Diplomarbeit and the work in the Ph.D.thesis.