Required Text: Spacetime and Geometry (Carroll) The link is to Sean Carroll's personal page about the book, which contains useful information about editions from different publishers (they are the same!)
Additional Reading (optional)
There are a large number of GR textbooks available, offering a variety of different perspectives. I list a few examples here. (When available I provide links to the goodreads web pages. I do that because they offer links to a variety of options for purchase, including used, but I DO NOT recommend the online reviews). I am trying to get these on reserve at the UCD library, but I find their system confusing and am not yet sure I have been successful.
NOTE: The books lised below are truly optional. The course itself will be grounded in the required text. I list these here in case you are seeking additional support for your studies from different perspectives, or are simply curious.
Introduction to General Relativity Gerard 't Hooft. An online textbook which gives a beautiful very physical and straightforward treatment. I was strongly tempted to use this as the main text for our course but favored Carrol because it contains more material.
Gravitation and Cosmology, Stephen Weinberg This highly regarded classic treatment emphasizes a field theory (vs geometrical) perspective.
Gravitation, Charles Misner, Kip Thorne and John wheeler This is a classic treatment with an extremely strong geometrical emphasis and a somewhat quirky presentation style.
Gravity, James Hartle An excellent textbook with a strong emphasis on observable general relativistic phenomena in the cosmos.
General Relativity, Robert Wald The most formal and mathematically rigorous of the books I list here.
Lectures on General Relativity and Cosmology. Pedro Ferreira. An excellent set of online notes which presents the basics in a very straightforward and efficient way. He also has a useful list of additional textbooks
Relativity: Special, General, and Cosmological Wolfgang Rindler A very thoughtful presentation which seems especially reflective on the background and motivations for some of the ideas.
General Relativity: A Concise Introduction Steve Carlip A brief introduction which discusses interconnections with different fields of physics, and current topics.
The Perfect Theory, Pedro Ferreira This is a popular level book (not a textbook) which gives a beautiful account of the history of general relativity from the earliest stages of its development through the current day. I thoroughly enjoyed reading this book and learned a lot about the history. (Truth in advertising: The author is a former PhD student of mine.)