This is the first comprehensive study for nearly 200 years of what remains of the writings of the Presocratic philosopher Philolaus of Croton (c. 470 385 BC). These fragments are crucial to our understanding of one of the most influential schools of ancient philosophy, the Pythagoreans, they also show close ties with the main lines of development of Presocratic thought, and represent a significant response to thinkers such as Parmenides and Anaxagoras. Professor Huffman presents the fragments and testimonia (including the spurious fragments in a separate section for reference) with accompanying translations and introductory chapters and interpretive commentary. He not only produces further argument for the authenticity of much that used to be neglected, but also undertakes a critique of Aristotle's testimony, opening the way for a quite new reading of fifth-century Pythagoreanism in general and of Philolaus in particular. Philolaus is revealed as a serious natural philosopher.