Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear and concise introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity.

‘ … written for final-year undergraduates mathematics or physics students … This short, elegant book describes the major ideas of special and general relativity with unprecedented clarity and mathematical depth.’

Source: Physics Today

‘Ludvigsen’s book provides us with an elegant modern introduction to Einstein’s general relativity; it is comprehensive, brief and very readable.’

Professor Sir Roger Penrose - Mathematical Institute, University of Oxford

‘ … a clear, clean, concise introduction to mathematical general relativity. It is a pleasure to see so many important topics discussed with such economy and care.’

Professor Bernard F. Schutz - Max Planck Institute for Gravitational Physics, Potsdam

‘The author has done a good work. The book is pedagogic and reads easily … this book is recommended for undergraduate studies both in physics and in mathematics and also for faculty libraries …’.

A. F. Ranada Source: European Journal of Physics

‘… the book introduces many refreshing novelties to the subject … Malcolm Ludvigsen’s book is never dull and this is a major thing in its favour’.

Graham S. Hall Source: General Relativity and Gravitation