This is a surprisingly compelling work of epistemology. In his first published monograph, Deleuze ingeniously reinvents Hume's system of philosophy not only to repudiate Kantian critical/transcendental philosophy but to rehabilitate empiricism as well on transcendental grounds.
What follows is an attempt to summarize the monograph's argument.
For most philosophers, the question is discovering the stable given of human nature, and the nature of the mind itself. Hume reverses this question by asking "How does the mind become human nature? How is the subject constituted in the given?"
For DH (Deleuze's Hume) the mind does not exist in itself. Rather, the mind is a collection of ideas that we refer to as the imagination. The imagination operates without constancy or uniformity, and it is a faculty guided the principles of association (the famous threesome of contiguity, resemblance, and causality). The principles of association provide a uniformity for the imagination, a system for the ideas so that they can acquire their own relations and thus become knowledge. It is in this process, the subject is born. And through the imaginative workings of the subject's fancy, the mind can travel beyond legitimate knowledge and acquire beliefs that are then regulated and corrected by various rules and principles. The subject is always that which is constituted within the given, but it is simultaneously that which transcends and moves beyond the given through the imagination.
There exists two axises that run through the subject. On the one hand you have the axis of ideas-association-transcendence-knowledge, but on the other hand you have the corollary axis of passions/affectations-belief-sympathy-morality whose principles and process are parallel to but incompletely independent of the generation of the subject.
What many philosophers have failed to grasp is that associations and affectations have no representative content. They cannot be thought in themselves but are merely activity. They go beyond the purview of reason. Deleuze underscores how reason is a limited faculty which only deals with parts, while feeling and sentiment deal with wholes. Reason cannot influence practice in the way that passion can.
What is perhaps most central is that DH argues that experience and habit are the two most powerful regulators of association and understanding. Experience always exists in the present as the reconstitution of the past (DH takes up temporality as duration here). Habit subsists through the difference of repetition, the aggregation of similar cases which allows the understanding to reason about experience. Because of this habit presupposes (and in some way is) experience. But at the same time their unity is not given.
Furthermore, DH repudiates Kant's rebuttal of Hume. Kant argues that Hume's empiricist philosophy makes the case that knowledge begins with and is derived from experience. And DH answers: Who wouldn't argue that we get knowledge from experience? Kant does not recognize that Hume has a completely different understanding of the nature of knowledge and experience.
Hume holds up the atomism of ideas and the associationism of ideas as completely independent phenomena with disparate generative principles. Hume does not believe genesis is absolutely determinative, he merely draws out their functional capacity to create the subject and the understanding. Empiricism is inherently based on the dualism between terms/atoms/ideas and associations/relations/human nature. The fundamental question of empiricism once again is "How is the subject constituted inside the given?" Kant is wrong to collapse the subject and the given to some presupposed unity or harmony. DH would contend that the given and the subject are not regulated by the same principles. Kant assumes this is the case. And this is primarily why his transcendental deduction fails.
Deleuze closes with the following lines:
"Here again, the fact is that the given never joins together its separate elements into a whole. In short, as we believe and invent, we turn the given into a nature. At this point Hume's philosophy reaches its ultimate point: Nature conforms to being. Human nature conforms to nature--but in what sense? Inside the given, we establish relations and form totalities. But the latter do not depend on the given, but rather on the principles we know; they are purely functional. And the functions agree with the hidden powers on which the given depends, although we do not know these powers. [...] Philosophy must constitute itself as the theory of we are doing, not as a theory of what there is. What we do has its principles; and being can only be grasped as the object of a synthetic relation with the very principles of what we do."