This book is a treatise on time and on background independence in physics. It first considers
how time is conceived of in each accepted paradigm of physics: Newtonian special relativity
quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover
uncovered between what is meant by time in QM and in GR. These differences jointly source the
Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of
the QM and GR paradigms as is required in particular for a background independent theory of
quantum gravity. A sizeable proportion of current quantum gravity programs - e.g.
geometrodynamical and loop quantum gravity approaches to quantum GR quantum cosmology
supergravity and M-theory - are background independent in this sense. This book's foundational
topic is thus furthermore of practical relevance in the ongoing development of quantum gravity
programs. This book shows moreover that eight of the nine facets of the Problem of Time already
occur upon entertaining background independence in classical (rather than quantum) physics. By
this development and interpreting shape theory as modelling background independence this book
further establishes background independence as a field of study. Background independent
mechanics as well as minisuperspace (spatially homogeneous) models of GR and perturbations
thereabout are used to illustrate these points. As hitherto formulated the different facets of
the Problem of Time greatly interfere with each others' attempted resolutions. This book
explains how none the less a local resolution of the Problem of Time can be arrived at after
various reconceptualizations of the facets and reformulations of their mathematical
implementation. Self-contained appendices on mathematical methods for basic and foundational
quantum gravity are included. Finally this book outlines how supergravity is refreshingly
different from GR as a realization of background independence and what background independence
entails at the topological level and beyond.
