Amazing Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject Three major applications of general relativity are then discussed black holes, perturbation theory and gravitational waves, and cosmology Students will learn the origin of how spacetime curves the Einstein equation and how matter moves through it the geodesic equation They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe A brief introduction to quantum field theory in curved spacetime is also included A student familiar with this book will be ready to tackle research level problems in gravitational physics. This is an outstanding textbook on general relativity It s very detailed, well written and the order of the topics is very well chosen, covering a wide range of themes The level is appropriate to graduate student, with a quite decent mathematical background.In particular, the first chapter is a review of special relativity a brief but clear summary, useful to become familiar with the use of the 4 vector notation, too The second and third chapters are committed to manifolds and curvature, and you have to learn the fundaments of differential geometry The chapters from fourth to seventh are focused on the real general relativity, from Einstein s equation to gravitational waves this is a quite advanced dissertation, and I think it is necessary to have a basic background from an introductory book The last two chapters are an introduction to cosmology brief, but pretty good and an introduction to quantum field theory in curved spacetime but I never read this chapter, sorry.Remark that the book contains ten 10 very useful appendixes on additional topics that are not debated in the ordinary chapters they are a good extension to examine in depth some themes in particular on a second reading.Very good binding and hardcover it s durable and solid, with a good value for money. This is a serious Graduate level text on GR well above the level of his many YouTube appearance Suggest that you also check out Mike Guidry s 2019 book Modern GR It focuses on all the many applications of GR Buy both books This is one of the best books on general relativity In my opinion it is somewhere between the classic Misner, Thorne, and Wheeler tome and Wald s General Relativity in its mathematical requirements I like the tone of the discussion of topics It is comprehensive enough to be useful in applications and leading to advanced studies.