Introduction to General Relativity
by Gerard 't Hooft
Publisher: Rinton Press 2010
Number of pages: 69
This book presents, in a natural and beautiful way, the general relativity as a scheme for describing the gravitational field and the equations it obeys. Starting from physical motivations, curved coordinates are introduced, and then the notion of an affine connection field is added. At a later step, the metric field is added. One then sees clearly how space and time get more and more structure, until finally Einstein's field equations logically come out.
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by Edmund Bertschinger - MIT
Working with GR requires some understanding of differential geometry. In this text we will develop the essential mathematics needed to describe physics in curved spacetime. These notes assume familiarity with special relativity.
by Robert Geroch - arXiv
All partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. We describe some broad features of systems of differential equations so formulated.
by Neil Lambert - King's College London
This course is meant as introduction to what is widely considered to be the most beautiful and imaginative physical theory ever devised: General Relativity. It is assumed that you have a reasonable knowledge of Special Relativity as well as tensors.
by Bernard F Schutz, Franco Ricci - arXiv
Notes of lectures for graduate students, covering the theory of linearized gravitational waves, their sources, and the prospects at the time for detecting gravitational waves. The lectures remain of interest for pedagogical reasons.