Preface; 1. Some basic mathematics; 2. Differentiable manifolds and tensors; 3. Lie derivatives and Lie groups; 4. Differential forms; 5. Applications in physics; 6. Connections for Riemannian manifolds and gauge theories; Appendix; Notation; Index.
Bernard Schutz has done research and teaching in general relativity and especially its applications in astronomy since 1970. He is an author of more than 170 publications, including three highly-regarded books published by Cambridge University Press: Geometrical Methods of Mathematical Physics, A First Course in General Relativity, and Gravity From the Ground Up. Schutz currently specialises in gravitational wave research, studying the theory of potential sources and designing new methods for analysing the data from current and planned detectors. He is a member of most of the current large-scale gravitational wave projects: GEO600 (operated by the AEI), LIGO, and LISA. Schutz is a Director of the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute (AEI), in Potsdam, Germany. He holds a part-time chair in Physics and Astronomy at Cardiff University, Wales, as well as Honorary Professorships at Potsdam and Hanover universities in Germany. Born and educated in the USA, he taught physics and astronomy for twenty years at Cardiff before moving to Germany. In 1998 he founded the open-access online journal Living Reviews in Relativity. In 2006 he was awarded the Amaldi Gold Medal of the Italian Society for Gravitation (SIGRAV). He is a Fellow of the American Physical Society and of the Institute of Physics, and a member of the German Academy of Natural Sciences Leopoldina and of the Royal Society of Arts and Sciences Uppsala.
'Although there are a welter of books where similar material can be
found, this book is the most lucid I have come across at this level
of exposition. It is eminently suitable for a graduate course
(indeed, the more academically able undergraduate should be about
to cope with most of it), and the applications should suffice to
persuade any physicist or applied mathematician of its importance
... Schutz's book is a triumph ...' The Times Higher Education
"...excellent. It would require a great deal of delving in the literature to produce equivalent treatments....a very useful introduction...." J. M. Stewart, Journal of Fluid Mechanics
"...Schutz has such a mastery of tthe material that it soon becomes clear that one is in authoritative hands....this book is the most lucid I have come across at this level of exposition. It is eminently suitable for a graduate course (indeed, the more academically able undergraduates should be able to cope with most of it), and the applications should suffice to persuade any physicist or applied mathematician of its importance." Ray d'Inverno, Times Higher Education Supplement