Who are our contemporaries today? Alain Badiou, Jean-Luc Nancy, or Giorgio Agamben, or the already neglected Althusser or Lacoue-Labarthe? From among the thinkers of the last great generation of the past century, who are the precursors whose voice is strong enough to speak to our present today? when the nature of time itself is uncertain: a time of mutation (Nancy), a change of epoch (Blanchot), an epoch without an epoch (Stiegler), or more catastrophically, the time of the geocide (Deguy)? Is it Bataille (Inner Experience) or Blanchot (The Writing of the Disaster) who anticipates the future that is already our present? Or Derrida who announced the unsurpassable dilemma of the law of hospitality? Announced a future to be presented only as a monstrosity? Or is it rather Deleuze, whose geo-philosophy already dispenses with the subject, privileges matter over spirit, and subordinates the great movements of peoples and animals of history and revolution, the political and the social as relative to the de- re-territorializing powers of the forces of the Earth? Or again, is it not philosophy but rather art that measures up to the intensity of the forces pressing against us in the present? The exhausted prose of Beckett, the broken verse of Celan? The stammer of Artaud? These are some of the questions that animate the writing in the aftermath of Agamben's influential essay What is the Contemporary? Critical reflections in the this first of two volumes work toward re-opening the question of contemporaneity today the concept and its time, its exigence and critical task, its actuality and actualizable possibility. The Concept and its Times is the first of a two-volume publication. The second volume, Art in the time that remains (978-1-84519-992-0), is due March 2020.