This textbook on the nature of space and time explains the new theory of Space Dynamics, which describes the dynamics of gravity as the evolution of conformal 3-dimensional geometry. Shape Dynamics is equivalent to Einstein's General Relativity in those situations in which the latter has been tested experimentally, but the theory is based on different first principles. It differs from General Relativity in certain extreme conditions. Shape Dynamics allows us to describe situations in which the spacetime picture is no longer adequate, such as in the presence of singularities, when the idealization of infinitesimal rods measuring scales and infinitesimal clocks measuring proper time fails. This tutorial book contains both a quick introduction for readers curious about Shape Dynamics, and a detailed walk-through of the historical and conceptual motivations for the theory, its logical development from first principles and a description of its present status. It includes an explanation of the origin of the theory, starting from problems posed first by Newton more than 300 years ago. The book will interest scientists from a large community including all foundational fields of physics, from quantum gravity to cosmology and quantum foundations, as well as researchers interested in foundations. The tutorial is sufficiently self-contained for students with some basic background in Lagrangian/Hamiltonian mechanics and General Relativity.

"Shape Dynamics is a new theory of gravity based on fewer and arguably more fundamental principles than the general theory of relativity. It reproduces all of the hitherto confirmed predictions of Einstein's theory but is much more restrictive in the solutions that it allows. Besides being therefore a more strongly predictive theory, it also reveals new aspects of gravity that have the potential to transform our understanding of the Big Bang and black holes. Flavio Mercati has been actively involved with the recent exciting developments of Shape Dynamics. His monograph includes a valuable account of the historical background to the theory and its conceptual underpinnings. It is an excellent introduction suitable for readers of a wide range of abilities: from physics and mathematics undergraduates, to active gravitational and cosmological researchers." - Julian Barbour, author of The Discovery of Dynamics and The End of Time