This book is a history of the development of mathematical astronomy in China, from the late third century BCE, to the early third century CE—a period often referred to as ‘early imperial China’. It narrates the changes in ways of understanding the movements of the heavens and the heavenly bodies that took place during those four and a half centuries, and tells the stories of the institutions and individuals involved in those changes. It gives clear explanations of technical practice in observation, instrumentation and calculation, and the steady accumulation of data over many years—but it centres on the activity of the individual human beings who observed the heavens, recorded what they saw, and made calculations to analyse and eventually make predictions about the motions of the celestial bodies. It is these individuals, their observations, their calculations and the words they left to us that provide the narrative thread that runs through this work. Throughout the book, the author gives clear translations of original material that allow the reader direct access to what the people in this book said about themselves and what they tried to do. This book is designed to be accessible to a broad readership interested in the history of science, the history of China and the comparative history of ancient cultures, while still being useful to specialists in the history of astronomy.