The work of Guattari/Deleuze can be used to try to understand how the current powers, the current forms of subjection and control, works and are exercised. But their work supports, apparently, multiple "usages"; usages among which proliferates the "academic", universitary. All of them omit, in general, three fundamental things: (a) the deep and tense dialogue that Guattari/Deleuze maintain with Marx and with Marxism, in order to actively intervene in concrete self-emancipatory social movements; (b) the double radical critique against the "Stateform" and against the capitalist mode of production (the "enterprise-form"); (c) the possibility of creating new ways of organization, new productive and re-productive social relations, new worlds of "possible", where the emergency of the State (as a social form of organization) and the emergency of the axiomatic of capitalism (as a relation and as a mode of production) be both conjured. In this 'First Part' we'll study (a) and (b); leaving (c) for a 'Second Part'.