This book focuses on one of the oldest and most fundamental questions in both physics and philosophy: the nature of time. It presents original theoretical physics research on the 'problem of time' in modern physics, in parallel with a new philosophical framework for the analysis of symmetry and evolution in physical theory, as well as new work on the early modern precursors to the problem of time. Contrary to the standard wisdom, this book argues that a substantive notion of time can, and should, be retained within a consistent formalism for modern physical theory. The book marshals an array of philosophical and formal tools to justify this claim and analyses its physical implications. This book is the first of a two-volume project articulating a new approach to the analysis of time in modern physical theory. The second volume will extend and apply this approach in the context of classical and quantum gravity including quantum cosmological models.