Eddington's The Mathematical Theory of Relativity is arguably the first comprehensive treatise on the mathematical and physical foundations of general relativity. As Prof. Ashtekar explained it in his excellent and informative Foreword "it is comprehensive on three fronts: Eddington systematically introduces the tools of differential geometry, explains the (then known) physical consequences of the theory with admirable clarity, and discusses in detail the conceptual underpinning of general relativity." The new publication of Eddington's book is justified not only by its historical value, but also by the fact that it still provides an original and detailed introduction to the deep physical ideas of general relativity and its mathematical formalism, whose "treatment throughout the monograph is clear, sharp and at the same time pedagogical" (from the Foreword).Eddington's enlightening exposition of general relativity "carries interesting lessons for contemporary researchers in gravitational science at all stages of their career. It is therefore fortunate that the Minkowski Institute Press is making this historic monograph easily available once again" (from the Foreword). NOTE: This book is not a re-publication of the scanned pages of the original publication; the text has been typeset in LaTeX.