In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights for such inequalities to be true. As a consequence, we establish Hardy, Hardy-Sobolev, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequalities and their critical versions on general connected Lie groups, which include both unimodular and non-unimodular cases in compact and… Expand