The rhizome is the organizing metaphor of A Thousand Plateaus, but the book is not primarily about rhizomes as such. It is about developing a conceptual vocabulary that can describe a world understood as fundamentally dynamic, multiple, and without a fixed center. The key concepts need to be understood in relation to each other.
An assemblage (agencement in French, which also carries connotations of arrangement and fitting-together) is Deleuze and Guattari's basic unit of analysis. An assemblage is not a thing but a functioning together: a temporary, contingent arrangement of heterogeneous elements, bodies, utterances, institutions, desires, territories, technical objects, that produces specific effects. A city is an assemblage. A romantic relationship is an assemblage. A military campaign is an assemblage. A musical performance is an assemblage. The important point is that the assemblage is not reducible to any of its components and is not unified by any single origin or purpose. It is what it does, not what it is.
Every assemblage has two dimensions. On one axis, there are content (bodies, objects, actions) and expression (signs, statements, language). On the other axis, there are processes of territorialization (the stabilization, stratification, and coding of the assemblage into recognizable forms) and deterritorialization (the loosening, destabilizing, or escaping of those forms). Every assemblage is always doing both: stabilizing itself and becoming unstable, forming territories and opening exits. This dual movement is central to Deleuze and Guattari's entire political and creative philosophy.
Lines are how they describe the trajectories available within and between assemblages. There are lines of molar segmentarity, the hard, rigid lines that organize life into fixed categories and territories (man/woman, citizen/foreigner, normal/pathological, worker/manager). These are the arboreal, tree-like lines. There are lines of molecular flexibility, softer, more fluid lines that blur the hard categories, allowing flows and becomings that the molar lines try to contain. And there are lines of flight (lignes de fuite), lines of genuine rupture, escape from the territory altogether, creation of something genuinely new. A line of flight is not escape into nowhere; it is a deterritorialization that opens new possibilities, new connections, new forms of life.
The concept of becoming is related. For Deleuze and Guattari, identity is not fixed. Persons, communities, and institutions are not stable essences but processes of becoming: always in movement, always being changed by their encounters, always capable of becoming-other. The canonical example is becoming-animal: not literally turning into an animal, but entering into a zone of intensity shared with an animal's mode of existence, the wolf-pack's distributed alertness, the bird's territorial song, the tick's radical simplicity of desire. Becoming does not mean imitation or resemblance. It means a genuine transformation of what one's experience and desire are like.
The plane of immanence, borrowed from Spinoza and developed through Deleuze's reading of Bergson, is the ontological backdrop: a flat, immanent field of all that exists, with no transcendent organizing principle above or behind it. There is no God, no Idea, no Foundation that determines what is possible from outside. There is only the plane itself, with its intensities, its speeds and slownesses, its lines and assemblages, its constant differentiation. This is what makes Deleuze and Guattari genuinely anti-humanist in the theoretical sense: there is no privileged human subject at the center of the plane of immanence, no transcendental consciousness that organizes experience from above. There are only assemblages of which human beings are part, and the question is always what kind of assemblage, what kind of connections, what kind of lines.