Gilles Deleuze's _Difference and Repetition_ (published in 1968) is a pivotal work, often considered his masterwork or a core text. It is a metaphysical treatise that fundamentally challenges traditional philosophical approaches. The book is structured around a central project: to critique the dominant image of thought in philosophy and develop an alternative that prioritizes difference and repetition. Here are some of the core concepts explored in _Difference and Repetition_: 1. **Critique of Representation and the Dogmatic Image of Thought:** A central aim of _Difference and Repetition_ is to critique the idea that thought should be understood in terms of the representation of an external reality. Deleuze argues against the "dogmatic image of thought" that has dominated the philosophical tradition from Plato to Kant. This image identifies thinking with knowing and assumes that knowledge is fundamentally a form of recognition. It presupposes a natural capacity for thought endowed with a talent for truth. Deleuze seeks to outline a nonrepresentational conception of thought. He suggests that philosophy, in its theory of thought, is in a position similar to modernist painting before its revolution, needing a shift from representation to abstraction. This move from representation to abstraction is seen not as a move towards conceptual abstraction in the traditional sense (e.g., Kant's universal concept), which grounds repetition in resemblance and represented qualities, but towards a different kind of concept grounded in action or an assemblage of predicates around an action. 2. **Difference in Itself:** A key concept is the idea of "difference in itself". Deleuze seeks to think difference directly, rather than subordinating it to identity. He argues that difference is not, and cannot be, thought in itself as long as it is subject to the requirements of representation, which typically involves comparing things to an identity, a genus, or an undetermined concept. Instead of understanding difference bilaterally in relation to unity, Deleuze understands it unilaterally in relation to zero. Difference becomes a substantial multiplicity of divergent and diffusive series. _Difference and Repetition_ begins with a statement on indifference, describing it as having two aspects: a black 'undifferentiated abyss' and a 'calm surface' of white nothingness. 3. **Repetition:** Deleuze distinguishes a profound kind of repetition from what he calls "bare" or "empty" repetition, which is based on resemblance or generality. The latter is tied to the representational image of thought. The book is concerned with a repetition that is not grounded in the generality of the concept and does not involve the simple repetition of the same or similar. Repetition, in the context of eternal return for instance, involves conceiving the same based on the different. It performs a practical selection among differences according to their capacity to produce and return. 4. **The Relationship between Difference and Repetition:** The book explores the deep, interconnected relationship between difference and repetition. The philosophy developed aims to be one of difference and repetition operating within a plane of immanence. The objective is to understand how repetition is produced on the basis of difference and how difference is selected on the basis of repetition. 5. **Transcendental Empiricism and the Ontology of the Question:** _Difference and Repetition_ outlines a theory of "transcendental problems" as the ground of thinking and the source of all truths. These problems are understood in a sense akin to Kant's Transcendental Ideas as problematic horizons, but are reconfigured by Deleuze. Problems are the "differential elements in thought, the genetic elements in the true". This view implies a twofold genesis: a logical genesis of truths as solutions to problems and a transcendental genesis of the act of thinking in discovering or constituting problems. This approach constitutes a "genetic transcendental philosophy" that accounts for the genesis of transcendental illusion as well as valid thought. It involves an "ontology of the question". Deleuze defends a "transcendental empiricism" where the existence of problems is an open question dependent on the field of thought in a given society at a given time, rather than being set by ahistorical reason or the nature of reality itself. 6. **Singularities:** Singularities are presented as key elements within the philosophy of difference. They are described as the "true transcendental events". In contrast to extensive individuals or generals, singularities are real, but concretely indifferent or abstract, elements that compose the creation of new functions. Deleuze, following Peirce and critiquing Aristotle and Kant, affirms an actually infinite world teeming with pre-individual singularities. 7. **Passive Syntheses:** Developed notably in the second chapter, passive synthesis is a process through which individuation occurs without presupposing a pre-existing identity. Instead, it presupposes an actual infinite or indeterminate chaos. This concept generalizes Hume's idea that repetition changes the mind through habit and expectation. Deleuze extends this, arguing that an organism is a sum of contractions, retentions, and expectations. Passive syntheses are external relations that are nonetheless inseparable from the terms they relate. 8. **The Virtual and The Actual:** _Difference and Repetition_ further develops the distinction between the virtual and the actual, building on Deleuze's reading of Bergson, particularly his theory of memory. The virtual is described as real without being actual. The actualization of the virtual leads to the creation of new functions. This distinction is crucial for understanding Deleuze's concept of time and memory, challenging the idea of memory as a mere repetition of past states or a storage of physical traces. Actualization involves a movement from past (virtual) to present (actual). The aim is to show how the syntheses of time are "ungrounded" in an open circle that produces the "absolutely different". 9. **Immanence:** The principle of immanence is fundamental to _Difference and Repetition_ and Deleuze's wider philosophy. The philosophy of difference and repetition operates within a plane of immanence, contrasting with philosophies that rely on transcendence (e.g., transcendent norms, values, or identities). Immanence means relations are external to the terms but not separate from them. The plane of immanence is understood as having no supplementary dimension, where the process of composition is apprehended in itself. Expression is seen as a composition or structure of being, resisting any move to transcendence. 10. **Multiplicity:** While more extensively explored in _A Thousand Plateaus_, the concept of multiplicity appears in _Difference and Repetition_. Deleuze's philosophy is characterized as a "logic of multiplicities". Multiplicities are defined by a variable number of dimensions that resist unification or universalization, contrasting with the metaphysical concept of essence. They are not given all at once but unfold progressively and are concrete and immanent to each other, forming the plane of immanence. This concept moves beyond the traditional opposition between the One and the many. In essence, _Difference and Repetition_ is a monumental work that seeks to overturn the traditional philosophical emphasis on identity, representation, and generality by developing a metaphysics centered on difference, repetition, singularities, passive syntheses, the virtual, and immanence. It offers a complex, intensive account of reality as dynamic, self-organizing, and perpetually producing the new, challenging the very foundations of how we understand thought and being.