INTRODUCTION As the inescapable reality of human co-existence is everyday faced in many different instances, artificial administrative borders appear to fade in importance when confronted with the increasingly integrated social interaction and resulting problems, whether it is the trans-border pollution, the management of water resources or the technological development that has led to easy and faster communications and travels. The need to face such reality has given rise to coordinated efforts among previously autonomous (at instances warring) communities of human beings. The emergence of "issues of global concern" has increasingly, moved the international community from a paradigm of co-existence into new-found ways of cooperation. In this regard, the fundamental question addressed in this research is of whether there is a (normative) Constitutional dimension of International Relations. International law, while regulating the relations of such communities, has attempted to encompass this exercise of public authority, increasing beyond the traditional politically organized (national) communities, into a new-found inter- dependence, as the complex multi-disciplinary phenomena of globalization have but been typically characterized by the de-territorialization of law, as overcoming former domestic solidarities. Naturally the question then turns to the debates around the terms and choices of such new-found normativety, which necessarily come to be referred to the postulation of a legitimacy quest in international law. Such question has been referred to the (material) "Constitutional dimension" of international law, in line with some instances of global accord (around the concept of ius cogens), which then appear to be designed at the acknowledgment and further development of a global cosmopolitan civitas. This matter shall be object of the Chapter I, whereby the Constitutional dimension of International Law, referred at least initially to the normative values of ius cogens norms, will be analysed, and the question on the correct terms of such quest tentatively answered. In this sense, the questions raised to the Constitution as the "legal statute of the political", traditionally referred to the legitimacy of public life shall be formulated at an increasingly global public life, which legitimation has traditionally been referred to different guises ofa Cosmopolitan project. The shortcomings of such a project have already been referred in national multi- cultural communities, but they take, on the global "public sphere", a founding importance in light of the "unevenness" of the power positions of the different actors. These undercurrents that take form on the global political interaction should be at the top of contemporary efforts aimed at the creation of a truly "inclusive" global political community. Chapter II shall attempt to demonstrate, precisely the political relevance of ensuring a relation with "alterity", from domestic multicultural communities to the global arena, on the assessment of a truly "legitimate" public violence, beyond the totalitarian pseudo-tolerance of existing normative models of democracy. One such global concern that has tragically come to portray the trials and errors of designing a truly global normativety is the international fight against international and trans-national crime , all the more after the 9.11.2001 events. This is but an example of the phenomenology that has come to illustrate the growing integration of human existence, on the one hand, and the terms of the normative response intent at curbing it, on the other. The particular terms of criminal intervention, a last resort tool in the state protection of (special) communitarian values due to its gravest consequences, impose a particular consensus in its design domestically illustrated by a Criminal Policy oriented by the Comprehensive Criminal Law Science , referred to a domestic constitution that ensures its procedural and axiological validation. The international consensus on the ICC Statute appeared in line with the referred (substantive) global Constitutional accord, which nevertheless left out the definition of a crime of "Terrorism". And it is precisely the uniform definition of terrorism, which continues to escape international lawyers and negotiators that illustrates the deliberative attempts and limitations of international normativety (and constitutionalism) and has hence been referred to an inductive approach. Chapter 111 shall precisely attempt to demonstrate that the international efforts to combat international terrorism are a good example of the exclusionary nature of international deliberation and the limits of a phenomenological normative consensus, particularly illustrated with regard to the international definition of terrorism. However, these efforts of fighting international terrorism go well beyond the problem of finding a global definition to the crime of terrorism, as they have also come to signal the emergence of a true "global governance" based on a real "global administrative space" and "global administrative law", which legitimation (at the hands of various uneven hegemonic prepositions) if solemnly referred to the traditional normative deliberationism shall be overly insufficient. These limitations on global normative decision-making have come to highlight the importance of a casuistic problem-solving normativety at the international realm, all the more so in light of the growing examples of last instance (judicial or not) decisions on this matter, both domestic and global (or of global consequences), as individuals are increasingly affected by such global use of public authority. These have been particularly important in the case of international terrorism, but they have also arisen in various different matters. In this sense, Chapter IV shall enquire into whether a principialist approach, with reference to a global "Inter- Constitutionality", to the need of ensuring a legitimate international public space is in order, or at all possible. Recent examples of international judicial decisions shall be referred to assess such a possibility. It is the radical importance of these questions, and the novelty that some recent developments present, that justify the present approach to matters that nowadays mark the debate on the sources of international law and more generally the general theory of international law and its perspectives. A humble reflexive intent animates this effort as the question on the (normative) Constitutional dimension of International Relations and International law remains (and most likely shall remain so for years to come) largely still unanswered.