In this course, dictated between the end of 1979 and the beginning of 1980, Gilles Deleuze demonstrates the effectiveness of the hypotheses and concepts he has created together with Félix Guattari in the series Capitalism and Schizophrenia to think with originality one of the most visited problems by the sciences social: the emergence and the relationship between state and capitalism. In the first part, from contemporary anthropological and archaeological research, and using marginalist economic theory to think about the possibility of exchange in the so-called primitive communities, discusses any evolutionary idea about the origin of the State proposing the hypothesis of a coexistence of diverse social formations even before the development of agriculture. The State appears as a capture device, a process of overcoding of flows, origin of both agriculture and money. But also flows that are decoded, such as the work of freedmen and private property. How can these flows, which are at the base of capitalism, compose a social formation despite being decoded? The second part of the course answers this question, in which Deleuze explains the notion of axiomatics in mathematics and in the framework of a "science policy". The characterization of capitalism as axiomatic will lead him to explore some classic themes, such as the limits of capitalist development or the difference between totalitarianism and social democracy, as well as contemporary issues such as the current type of war or the deterritorialization of inequality between center and periphery economic Spills II. Apparatus of State and capitalist axiomatic condenses and thoroughly develops sociohistorical and more directly political theses that appear sometimes dispersed and implicit in The Anti-Oedipus and Thousand Plateaus.