Before this book I read a few introductory books on this subject, without really grasping the core of general relativity.
It has to be pointed out that general relativity cannot be fully appreciated without a good undestanding of the mathematics involved. Thanks to the first part of the book - which is a concise but illuminating introduction to differential geometry, tensor algebra on so on - the reader can really handle the required mathematical tools. For instance, contravariant and covariant components are magnificently explained, as well as the concept of tensor (abstract mathematical entity whose nature does not depend on the local coordinate frame, whereas whose representation does strongly depend on it).
The rest of the book is a superb and outstanding presentation of classical and recent applications of general relativity to astrophysics and cosmology.
In short, I really recommend this book to anyone who is interested in this subject. I would strongly suggest not to waste time with other references before having read this.
This is a nice introduction to the subject. It is at undergraduate level, and assumes knowledge of classical mechanics and differential equations. It starts with special relativity and the Lorentz transformation, then goes on to introduce differential geometry - really for physicists. There are no one-forms, this is not the 'modern' differential geometry of Schutz. Instead, there are the covariant and contravariant vectors and tensors of old fashioned GR, and the authors explain them in a clear-to-understand way. This really helps later in the book with Schwarzschild black holes, stellar interiors and cosmology. If you want to understand GR and don't care about analysis-style proofs, get this book.
This is an excellent book if you haven't studied general relativity before. It starts off from special relativity, then develops the mathematical formalism needed for GR, then goes on and treats forces and metrics in GR.
I found it really well written, both with very thorough maths but most importantly with good geometric interpretations of the mathematics, which enable you to lock it down in your memory very easily.
The only problem I see is that it should more or less be read with the chapters in the right order, you cannot sudenly skip to the electromagnetism chapter as there are a lot of references to concepts explained in previous chapters. This means that it takes a bit to read it, though the reading is relatively smooth and you can keep a "sustained pace". I didn't read as much of the book as I would have liked as it does take quite a while, but I still got a very high mark on the exam.
As someone to got a smattering of tensor calculus, differential geometry and General relativity at university (many years ago), it was great to refresh (and expand) my knowledge of the basics with this clearly written exposition of GR.
The explanation of manifolds and the concepts of covariant and contravariant tensors/vectors relies as much as possible on intuitive description while not sacrificing too much mathematical rigor. The book moves smoothly to more advanced topics (Lagrangian formulations, Kerr metrics, Schwarzschild solutions) and the reader comes to understand some of the reasons why the ultimate fate of the universe is still an open question...
Great introduction to the subject with sufficient mathematical rigor, especially on some of the more complicated proofs. However some of the mathematical reasoning assumes prior knowledge and so skipped---better if these are provided in answers to the exercises or web-based references of proofs are shown. I had to look up proofs in other books. Quite a lot of algebra skipped in the derivations in the chapter on variational methods, especially on omitted second order terms, which I find rather difficult to follow with quite a lot of guessing.
(Note: Only about 30% through the book). A very good introduction to General Relativity for Engineers and Scientists. Unusually for a textbook covering a subject at this level, it is possible to follow every step in the development, and derive nearly all the equations.Covers the basis vectors very well, although a geometric interpretation in 3D would have been helpful. Have found this book plus Kenyon's General Relativity a good combination..
I'm not very far through the book yet, so won't comment on the content, but as someone who has bought many maths/physics textbooks for Kindle, I must point out that the transcription of both inline and standalone maths is as impressive as any I've seen.