Lilley, Sam. Discovering
Relativity for Yourself. Cambridge University Press, 1981.
The Epstein book is a must-read for anyone interested in relativity.
I adore this book. Even professionals already familiar with the traditional
approaches to teaching relativity should read this book, as it provides
unique insights into the theoretical concepts that you just cannot find
anywhere else. It is an absolute model of clear and simple writing. While
it is remarkable enough as an exposition on special relativity, it accomplishes
a near-miracle in its simple, intuitive explanations of general relativity.
Epstein has said that there is a simple way to explain anything, it's just
very difficult to find it, and in this book, he proves it. Click on the
link provided to purchase the book from Amazon.com.
The Lilley book is unfortunately out of print, but click on the link provided to use Amazon.com's used book locator service (or check your local university library). It provides a very accessible introduction to the Minkowski diagram as a way of understanding special relativity. It gets more into the mathematics than Epstein's book, but is still very accessible, and any mathematics that goes beyond the simple high-school level is explained from scratch. It also complements the Epstein book nicely because it uses Minkowski diagrams, which are more standard than Epstein's. The two approaches use different tricks to display Einsteinian 4-D space on a Euclidean 2-D page, and so your intuition will be all the better for having studied both of them. The Lilley book also gets into the actual mathematics of general relativity, but without delving into the intricacies of tensor calculus. To achieve such simplification, Lilley describes a theory that is actually not quite general relativity, but is a little bit different. However, he makes it clear where his simplifying assumptions lie.
I am not yet advanced enough to know the best books that actually delve into the tensor calculus of general relativity. Likewise for quantum cosmology, which attempts to combine general relativity and quantum mechanics (but see my page on quantum theory books for some excellent nonmathematical books on quantum mechanics in general). Although I do not know of any nonmathematical layman's introduction to quantum cosmology that really does it any justice (certainly nothing that even approaches the sophistication of Epstein), I would love to hear from anyone else who does (please email me). However, I can suggest the following books, which look like they might be good, although I cannot as yet recommend them (note that they do require some university-level mathematics):
Kontopoulos, Geåorgios Iåoannou & Dimitrios Kotsakis. Cosmology: the structure and evolution of the universe. M. Petrou & P.L. Palmer (Trans.), Springer-Verlag, 1984.