This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.

'The strength of Gray’s book lies in his concern to provide friendly, pedagogical explanations for many tricky features of the theory, starting from a basic level, and his informal style will be welcomed by the less confident reader.'

Peter J. Bussey Source: Contemporary Physics

'... this book marks a welcome move to shorter, more focussed introductions to General Relativity aimed at undergraduate students. As the mathematical half of a full GR course it works well, but perhaps a less abstract approach and greater emphasis on the geometrical nature of the theory might appeal more to some readers.'

Andrew Taylor Source: The Observatory

‘This book is part of the Cambridge 'Student’s Guide' series. It is based on a 10 lecture course the author taught at the University of Glasgow. The book is mostly about introducing the math needed to reach the discussion of the Einstein equation.’

Jorge Pullin Source: zbMATH