Islam has become a major topic of media and academic attention. Glosses of current emphases, such as “conservative revolution” and “Islamic radicalism”, go some way to explain this topicality, but not the phenomena and their phenomenologies. Against the conceptual fog and theoretical mist surrounding these issues, IRENE proposes the ethnography of normative practices referring to Islam. It means attending to little and local truths, always singular and contingent, in the frame of which norms referring to Islam are contextually, though most often incidentally, used. We live in times where people resort to extremely diversified norms, which not only interlace but also influence and transform each other. It is precisely IRENE’s aim to describe how people ordinarily resort to multiple normative repertoires in a largely non-problematic way; how apparent contradictions are practically reduced; how new norms emerge, which can serve as support for action and justification; and how they come to be somehow naturalized. In other words: how Islam is lived in a diffuse way, as a background whose constraints vary considerably from place to place. The attention was generally drawn on all that reflected Islam’s hyper-normativity in political, legal and economic matters. However, the level of diffuse normativity remains under-explored, even though it is at this level that the majority’s practices and therefore deep social transformations unfold. Our analysis focuses on the ordinary modes of practical reasoning through the exploration of normative domains (the “good”, the “just”, the “true”, the “beautiful”) within Muslim contexts. The empirical part of the research is conducted in a dozen of fields in which, in the ordinary lives of Muslims in North Africa and Western Europe, various norms interplay. IRENE’s general ambition is thus to produce a social science of Islam that addresses the phenomenon of normativity, which is at the heart of contemporary Muslim communities’ social life.