Feynman, Richard P. QED:
the strange theory of light and matter. Princeton U. Press, Princeton,
1985.
Mattuck, Richard D. A
Guide to Feynman Diagrams in the Many-Body Problem (2nd. Ed.).
Dover Publications, New York, 1976.
Finding the right books from which to learn quantum mechanics from scratch is extremely difficult, and took me a long time, searching through many so-called introductory texts that provided next to no conceptual intuition about the subject at all (one wonders if their authors have any such conception to begin with). Many of the nonmathematical treatments, written for the layman, are deceptive and not true to their subject, or worse yet are steeped in mysticism. The above books were absolutely essential to the development of my current understanding of the field, and each is a rare example of excellence in teaching. You can follow the links provided to purchase the books from Amazon.com.
I have included two introductory books for the educated layman. These require very little math, and are both brilliantly written. Even if you do not get any more advanced than these two books, you will have been introduced to all the major concepts of the field, and may well end up with a better grasp of the philosophical issues than many professionals. I list the Herbert book first, since strictly speaking it covers less ground and is thus more introductory. However, the Feynman book is very accessible, and you might even prefer to read it first, depending on your background and tastes. The two books complement each other nicely in their rather different approaches to the material, and could also be read concurrently.
I have included two additional books on a more advanced level. These require more mathematical background, at the introductory university or advanced high-school level. Both are successfully conceptual and mathematical at the same time, a rare combination. The Chester book introduces the standard mathematical devices of quantum theory, while the Mattuck book explains more advanced concepts, and thus the books are listed in that order. However, you should not read them in sequence like that. Read the introductory chapters of both books before attempting to read the more advanced material in either. The introductory material in the Mattuck book is quite conceptual and nonmathematical, and so could even be read before the opening chapters of the Chester book, although exactly what route you follow will, again, depend on your background and tastes.
I treasure each of these books more than I can tell you, and cannot imagine what my world view would be like without them.
In between reading the nonmathematical books and the more advanced books (or even before), you might want to take a look at my paper, Quantum Phenomenology, which introduces the basic idea of the Dirac notation used in the Chester book, but in an a priori philosophical context. As such, it could be useful as a prelude to the Chester book, but the reader should keep in mind that the "quantum" theory developed is not quantum mechanics, but an a priori, nonempirical theory of physics that just happens (coincidence?) to have a very similar structure to quantum mechanics. Hence, my treatment involves particular philosophical commitments and is thus more speculative and not as "standard" as the four books above. Another introduction to Dirac notation that might be useful to read before getting into the Chester book is David Albert's Quantum Mechanics and Experience, Chapter 2, which is excellant and intermediate between my paper and Chester's book in difficulty (the rest of Albert's book is also nice, but keep in mind that it is more a defence of Albert's particular philosophical interpretation than a general introduction to quantum mechanics).
I am not yet advanced enough to know the best books on quantum cosmology, the attempt to combine quantum mechanics and general relativity. However, see my page on relativity books for some suggestions.