This work will critically address Hans-Hermann Hoppe's anarcho-capitalist theory. In this paper, I'll start exegeting this author's libertarian thought, presenting his concepts and hypotheses as they have been published in many of his works in economics and political theory. I'll discuss the concepts of libertarianism, the State, humanity, time preference and natural order. I'll also present his reading of history, woven from a praxeological perspective, that foresees a dark future for men and women if States are not dismantled and the anarcho-capitalist utopia realized. I'll discuss the path that the author considers to be the most correct to abolish states and replace their sovereignty with privately-owned security, defense, and justice firms that are competitive and non-monopolistic. In the scope of this qualification, I'll make a brief comparative analysis between the political theory of Thomas Hobbes and that of Hans-Hermann Hoppe. The final chapter addresses the hypothesis that anarcho-capitalist orders and competitive justice systems existed and still exist today, but do not necessarily produce the pacifying and civilizing effects pointed out by Hoppe.