Auguste Comte is ostensibly the world’s most famous classifier of the sciences in modern history. His whole life was dedicated to establishing a classification that conformed to the ‘positivist’ (non-theological and non-metaphysical) principles he settled on after working with early nineteenth-century French social reformer Henri de Saint-Simon. This article first probes the background to Comte’s classifying of the sciences, discussing French and German influences, and the effect of the phrenological movement on his special attitude to psychology and social life. Central sections of the article concern the basic and most mature ordering of the sciences according to his fundamental Course of lectures on classification (1830-42), the development of a tableau to cover psychological issues, and attempts at tables to synthesize his ordering and draw out their implications for socio-political reform and the Church of Humanity he founded. Concluding sections cover key binding principles of his classificatory work, as well as matters of reception, influence, and critical response.