Suitable for a student who has a background in undergrad general relativity.
What do you mean by „modified theories of gravity” exactly? What exactly out of GR did you learn in school?
You may be thinking of Modified Newtonian Dynamics also known as MOND, rather than "modified theory of gravity". I think the term MOND or modified Newtonian dynamics, is higher regarded than modified theory of gravity. I do not know any textbooks on MOND off-hand, but there may be a few
Why should one write one since this speculation is ruled out by observations, as far as I know?
I, too, am unsure as to what binbags wants, but I don't think that it is MOND. A possibility is "Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics" by Capozziello and Faraoni, which emphasizes f(R) theories of gravity,
Also there is "Classical and Quantum Cosmology" by Calcagni,
This book has a brief survey of various theories of gravity in the last few sections of chapter 7, and then devotes a number of chapters to approaches to quantum gravity and quantum cosmology.
Use Amazon's Look Inside feature to look at the Tables of Contents of these books.
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