What are some of the differences between and among Euclidean, Riemannian and Lobachevskian geometries?

The Euclidean geometry is a geometry of flat space, while Riemannian, Lobachevski and also Gauss´s geometries which are historically and scientifically connected are for curved spaces, they are referred to as non-euclidean geometries too, because their postulates differs from euclidean geometry postulates, mainly the parallel postulate.